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True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.Each antiderivative of an $n$ th-degree polynomial function is an $(n+1)$ th-degree polynomial function.

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $p(x)$ is a polynomial function, then $p$ has exactly one antiderivative whose graph contains the origin.

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $F(x)$ and $G(x)$ are antiderivatives of $f(x),$ then

$$F(x)=G(x)+C$$

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$f^{\prime}(x)=g(x),$ then $\int g(x) d x=f(x)+C$$

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$\int f(x) g(x) d x=\left(\int f(x) d x\right)\left(\int g(x) d x\right)$

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The antiderivative of $f(x)$ is unique.

false

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True or False? In Exercises $73-76,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $f$ is undefined at $x=c$ , then the limit of $f(x)$ as $x$ approaches $c$ does not exist.

True or False? In Exercises $63-68$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$\int_{a}^{b} f(x) g(x) d x=\left[\int_{a}^{b} f(x) d x\right]\left[\int_{a}^{b} g(x) d x\right]$$

True or False? In Exercises $77-79$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $y$ is a function of $t$ and $x$ is a function of $t,$ then $y$ is a function of $x .$

TRUE OR FALSE? In Exercises 77 and 78, determine whether the statement is true or false. Justify your answer.

If $f(x) = x + 1$ and $g(x) = 6x$, then $(f \circ g)(x) = (g \circ f)(x)$.

True or False? In Exercises $85-90$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $f(x)=-g(x)+b,$ then $f^{\prime}(x)=-g^{\prime}(x)$

True or False? In Exercises $75-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$\begin{array}{l}{\text { The graph of every cubic polynomial has precisely one point }} \\ {\text { of inflection. }}\end{array}$

For the following exercises, determine whether the statement is true or false. Either prove it is true or find a counterexample if it is false.If $f(x)$ is the antiderivative of $v(x),$ then $(f(x))^{2}$ is the antiderivative of $(v(x))^{2}$ .

If you are given two functions $f(x)$ and $g(x)$, you can calculate $(f \circ g)(x)$ if and only if the range of $g$ is a subset of the domain of $f$.

True or False? In Exercises $63-68$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$\int_{a}^{b}[f(x)+g(x)] d x=\int_{a}^{b} f(x) d x+\int_{a}^{b} g(x) d x$$

True or False? In Exercises $83 - 86$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If the area of the region bounded by the graphs of $f$ and $g$ is $1 ,$ then the area of the region bounded by the graphs of$h ( x ) = f ( x ) + C$ and $k ( x ) = g ( x ) + C$ is also $1 .$

True or False? In Exercises $83-86$ , determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.If $f^{\prime \prime}(x)<0$ for all real numbers $x,$ then $f$ decreases withoutbound.

True or False? In Exercises $83 - 86$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If$$\int _ { a } ^ { b } [ f ( x ) - g ( x ) ] d x = A$$then$$\int _ { a } ^ { b } [ g ( x ) - f ( x ) ] d x = - A$$

True or False? In Exercises 81-86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $$\lim _{x \rightarrow \infty} f(x)=L, \text { then } \int_{0}^{\infty} f(x) d x$$

TRUE OR FALSE? In Exercises 75 and 76, determine whether the statement is true or false. Justify your answer.

The slope of the graph of $y=x^2$ is different at every point on the graph of $f$.

True or False? In Exercises $83-86$ , determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.Every polynomial function has an absolute maximum and anabsolute minimum on $(-\infty, \infty).$

True or False? In Exercises 65-68, determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false. The graph of a function cannot cross a vertical asymptote.

True or False? In Exercises $91-96$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The function $f(x)=x$ has no extrema on any open interval.

True or False? In Exercises 89 and 90 , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.\begin{equation}\text { If }f \text { is an even function, then } f^{-1}\end{equation}

True or False? In Exercises $83-86$ , determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.The slope of the graph of the inverse tangent function is positive for all $x.$

True or False? In Exercises 87 and 88, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.A slope field shows one particular solution of a differential equation.

TRUE OR FALSE? In Exercises 59-62, determine whether the statement is true or false. Justify your answer.

If $f(x)$ increases without bound as $x$ approaches $c$, then the limit of $f(x)$ exists.

In Exercises 71 and 72, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$\int \frac{d x}{25+x^{2}}=\frac{1}{25} \arctan \frac{x}{25}+C$$

TRUE OR FALSE? In Exercises 81-84, determine whether the statement is true or false. Justify your answer.

The graphs of

$f(x) = |x| + 6$

and

$f(x) = |-x| + 6$

are identical.

True or False? In Exercises $83-86$ , determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.Every rational function has a slant asymptote.

True or False? In Exercises $49-53,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $y$ is differentiable, then$$\lim _{\Delta x \rightarrow 0}(\Delta y-d y)=0$$

For the following exercises, determine whether the statement is true or false. Either prove it is true or find a counterexample if it is false.If $f(x)$ is the antiderivative of $v(x),$ then $f(2 x)$ is the antiderivative of $v(2 x)$ .

TRUE OR FALSE? In Exercises 85 and 86, determine whether the statement is true or false. Justify your answer.

If $f(c) = L$, then $\lim_{x \to c}\ f(x) = L$

True or False? In Exercises $77-80$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. Amplitude is always positive

True or False? In Exercises $73-76$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $$\lim _{x \rightarrow c} f(x)=L,$ then $f(c)=L$$

TRUE OR FALSE? In Exercises 103 and 104, determine whether the statement is true or false. Justify your answer.

If $f$ is an even function, then $f^{-1}$ exists.

True or False? In Exercises $85-90$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $f(x)=0,$ then $f^{\prime}(x)$ is undefined.

True or False? In Exercises $83-86$ , determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.The range of $$y=\arcsin x [0, \pi]$$

True or False? In Exercises $73-76$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $$f(c)=L,$ then $\lim _{\mathrm{lim}} f(x)=L$$

TRUE OR FALSE? In Exercises 69 and 70, determine whether the statement is true or false. Justify your answer.

If $y$ is a function of $t$, and $x$ is a function of $t$, then $y$ must be a function of $x$.

TRUE OR FALSE? In Exercises 73-76, determine whether the statement is true or false. Justify your answer.

If $D\neq0$ and $E\neq0$, then the graph of $x^2-y^2+Dx+Ey=0$ is a hyperbola.

True or False? In Exercises 73 and $74,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $f$ is continuous and nonnegative on $[a, b],$ then the limits as $n \rightarrow \infty$ of its lower sum $s(n)$ and upper sum $S(n)$ both exist and are equal.

True or False? In Exercises $91-96$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The relative maxima of the function $f$ are $f(1)=4$ and $f(3)=10 .$ Therefore, $f$ has at least one minimum for some $x$ in the interval $(1,3) .$

True or False? In Exercises $85-90$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $f^{\prime}(x)=g^{\prime}(x),$ then $f(x)=g(x)$

True or False? In Exercises 81-86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$\begin{array}{l}{\text { If the graph of } f \text { is symmetric with respect to the origin or the }} \\ {y \text { -axis, then } \int_{0}^{\infty} f(x) d x \text { converges if and only if } \int_{-\infty}^{\infty} f(x) d x} \\ {\text { converges. }}\end{array}$$

True or False? In Exercises $75-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $b^{2}-4 a c>0$ and $a \neq 0,$ then the graph of$$y=a x^{2}+b x+c$$

True or False? In Exercises 81-86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$\begin{array}{l}{\text { If } f \text { is continuous on }[0, \infty) \text { and } \lim _{x \rightarrow \infty} f(x)=0, \text { then } \int_{0}^{\infty} f(x) d x} \\ {\text { converges. }}\end{array}$$

True or False? In Exercises $83-86$ , determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.$$\frac{d}{d x}[\arctan (\tan x)]=1$$ for all $x$ in the domain.

True or False? In Exercises 81-86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$\begin{array}{l}{\text { If } f \text { is continuous on }[0, \infty) \text { and } \int_{0}^{\infty} f(x) d x \text { diverges, then }} \\ {\lim _{x \rightarrow \infty} f(x) \neq 0}\end{array}$$

True or False? In Exercises $91-96,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$0.75=0.749999 \ldots$$

TRUE OR FALSE? In Exercises 95-97, determine whether the statement is true or false. Justify your answer.

The graph of the function given by $f(x) =\ sin(x+2\pi)$ translates the graph of $f(x) =\ sin\ x$ exactly one period to the right so that the two graphs look identical.

True or False? In Exercises $83-86$ , determine whether the statement is true or false. If it is false, explain why or give anexample that shows it is false.$$\arcsin ^{2} x+\arccos ^{2} x=1$$

True or False? In Exercises $93-98$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$\int x\left(x^{2}+1\right) d x=\frac{1}{2} x^{2}\left(\frac{1}{3} x^{3}+x\right)+C$$

True or False? In Exercises $97-100$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$$\ln \left|\cos \theta^{2}\right|=\ln \left(\cos \theta^{2}\right)$$

True or False? In Exercises $87-92,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.It is possible for a parabola to intersect its directrix.

True or False? In Exercises $49-53,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If $y=f(x), f$ is increasing and differentiable, and $\Delta x>0,$then $\Delta y \geq d y .$

TRUE OR FALSE? In Exercises 77-82, determine whether the statement is true or false. Justify your answer.

$tan[(5^\circ)^2] = tan^2\ 5^\circ$

If $(-4,-5)$ is a point on a graph that is symmetric with respect to the $x$ -axis, then $(4,-5)$ is also a point on the graph.

If $b^{2}-4 a c=0$ and $a \neq 0,$ then the graph of$$y=a x^{2}+b x+c$$has only one $x$ -intercept.

If $(-4,-5)$ is a point on a graph that is symmetric with respect to the $y$ -axis, then $(4,-5)$ is also a point on the graph.

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## Recommended Questions

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $F(x)$ and $G(x)$ are antiderivatives of $f(x),$ then

$$F(x)=G(x)+C$$

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $p(x)$ is a polynomial function, then $p$ has exactly one antiderivative whose graph contains the origin.

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

Each antiderivative of an $n$ th-degree polynomial function is an $(n+1)$ th-degree polynomial function.

True or False? In Exercises $73-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$\int f(x) g(x) d x=\left(\int f(x) d x\right)\left(\int g(x) d x\right)$

True or False? In Exercises $73-76,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $f$ is undefined at $x=c$ , then the limit of $f(x)$ as $x$ approaches $c$ does not exist.

True or False? In Exercises $63-68$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$\int_{a}^{b} f(x) g(x) d x=\left[\int_{a}^{b} f(x) d x\right]\left[\int_{a}^{b} g(x) d x\right]$$

True or False? In Exercises $77-79$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $y$ is a function of $t$ and $x$ is a function of $t,$ then $y$ is a function of $x .$

TRUE OR FALSE? In Exercises 77 and 78, determine whether the statement is true or false. Justify your answer.

If $f(x) = x + 1$ and $g(x) = 6x$, then $(f \circ g)(x) = (g \circ f)(x)$.

True or False? In Exercises $85-90$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $f(x)=-g(x)+b,$ then $f^{\prime}(x)=-g^{\prime}(x)$

True or False? In Exercises $75-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.$\begin{array}{l}{\text { The graph of every cubic polynomial has precisely one point }} \\ {\text { of inflection. }}\end{array}$

For the following exercises, determine whether the statement is true or false. Either prove it is true or find a counterexample if it is false.

If $f(x)$ is the antiderivative of $v(x),$ then $(f(x))^{2}$ is the antiderivative of $(v(x))^{2}$ .

TRUE OR FALSE? In Exercises 77 and 78, determine whether the statement is true or false. Justify your answer.

If you are given two functions $f(x)$ and $g(x)$, you can calculate $(f \circ g)(x)$ if and only if the range of $g$ is a subset of the domain of $f$.

True or False? In Exercises $63-68$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$\int_{a}^{b}[f(x)+g(x)] d x=\int_{a}^{b} f(x) d x+\int_{a}^{b} g(x) d x$$

True or False? In Exercises $83 - 86$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If the area of the region bounded by the graphs of $f$ and $g$ is $1 ,$ then the area of the region bounded by the graphs of

$h ( x ) = f ( x ) + C$ and $k ( x ) = g ( x ) + C$ is also $1 .$

True or False? In Exercises $83-86$ , determine whether the

statement is true or false. If it is false, explain why or give an

example that shows it is false.

If $f^{\prime \prime}(x)<0$ for all real numbers $x,$ then $f$ decreases without

bound.

True or False? In Exercises $83 - 86$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If

$$\int _ { a } ^ { b } [ f ( x ) - g ( x ) ] d x = A$$

then

$$\int _ { a } ^ { b } [ g ( x ) - f ( x ) ] d x = - A$$

True or False? In Exercises 81-86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $$\lim _{x \rightarrow \infty} f(x)=L, \text { then } \int_{0}^{\infty} f(x) d x$$

TRUE OR FALSE? In Exercises 75 and 76, determine whether the statement is true or false. Justify your answer.

The slope of the graph of $y=x^2$ is different at every point on the graph of $f$.

True or False? In Exercises $83-86$ , determine whether the

statement is true or false. If it is false, explain why or give an

example that shows it is false.

Every polynomial function has an absolute maximum and an

absolute minimum on $(-\infty, \infty).$

True or False? In Exercises 65-68, determine whether the

statement is true or false. If it is false, explain why or give an

example that shows it is false.

The graph of a function cannot cross a vertical asymptote.

True or False? In Exercises $91-96$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

The function $f(x)=x$ has no extrema on any open interval.

True or False? In Exercises 89 and 90 , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

\begin{equation}\text { If }f \text { is an even function, then } f^{-1}\end{equation}

True or False? In Exercises $83-86$ , determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.

The slope of the graph of the inverse tangent function is positive for all $x.$

True or False? In Exercises 87 and 88, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

A slope field shows one particular solution of a differential equation.

TRUE OR FALSE? In Exercises 59-62, determine whether the statement is true or false. Justify your answer.

If $f(x)$ increases without bound as $x$ approaches $c$, then the limit of $f(x)$ exists.

In Exercises 71 and 72, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$\int \frac{d x}{25+x^{2}}=\frac{1}{25} \arctan \frac{x}{25}+C$$

TRUE OR FALSE? In Exercises 81-84, determine whether the statement is true or false. Justify your answer.

The graphs of

$f(x) = |x| + 6$

and

$f(x) = |-x| + 6$

are identical.

True or False? In Exercises $83-86$ , determine whether the

statement is true or false. If it is false, explain why or give an

example that shows it is false.

Every rational function has a slant asymptote.

True or False? In Exercises $49-53,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $y$ is differentiable, then$$\lim _{\Delta x \rightarrow 0}(\Delta y-d y)=0$$

For the following exercises, determine whether the statement is true or false. Either prove it is true or find a counterexample if it is false.

If $f(x)$ is the antiderivative of $v(x),$ then $f(2 x)$ is the antiderivative of $v(2 x)$ .

TRUE OR FALSE? In Exercises 85 and 86, determine whether the statement is true or false. Justify your answer.

If $f(c) = L$, then $\lim_{x \to c}\ f(x) = L$

True or False? In Exercises $77-80$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

Amplitude is always positive

True or False? In Exercises $73-76$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $$\lim _{x \rightarrow c} f(x)=L,$ then $f(c)=L$$

TRUE OR FALSE? In Exercises 103 and 104, determine whether the statement is true or false. Justify your answer.

If $f$ is an even function, then $f^{-1}$ exists.

True or False? In Exercises $85-90$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $f(x)=0,$ then $f^{\prime}(x)$ is undefined.

True or False? In Exercises $83-86$ , determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.

The range of $$y=\arcsin x [0, \pi]$$

True or False? In Exercises $73-76$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $$f(c)=L,$ then $\lim _{\mathrm{lim}} f(x)=L$$

TRUE OR FALSE? In Exercises 69 and 70, determine whether the statement is true or false. Justify your answer.

If $y$ is a function of $t$, and $x$ is a function of $t$, then $y$ must be a function of $x$.

TRUE OR FALSE? In Exercises 73-76, determine whether the statement is true or false. Justify your answer.

If $D\neq0$ and $E\neq0$, then the graph of $x^2-y^2+Dx+Ey=0$ is a hyperbola.

True or False? In Exercises 73 and $74,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $f$ is continuous and nonnegative on $[a, b],$ then the limits as $n \rightarrow \infty$ of its lower sum $s(n)$ and upper sum $S(n)$ both exist and are equal.

True or False? In Exercises $91-96$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

The relative maxima of the function $f$ are $f(1)=4$ and $f(3)=10 .$ Therefore, $f$ has at least one minimum for some $x$ in the interval $(1,3) .$

True or False? In Exercises $85-90$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $f^{\prime}(x)=g^{\prime}(x),$ then $f(x)=g(x)$

True or False? In Exercises 81-86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$\begin{array}{l}{\text { If the graph of } f \text { is symmetric with respect to the origin or the }} \\ {y \text { -axis, then } \int_{0}^{\infty} f(x) d x \text { converges if and only if } \int_{-\infty}^{\infty} f(x) d x} \\ {\text { converges. }}\end{array}$$

True or False? In Exercises $75-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $b^{2}-4 a c>0$ and $a \neq 0,$ then the graph of

$$y=a x^{2}+b x+c$$

True or False? In Exercises 81-86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$\begin{array}{l}{\text { If } f \text { is continuous on }[0, \infty) \text { and } \lim _{x \rightarrow \infty} f(x)=0, \text { then } \int_{0}^{\infty} f(x) d x} \\ {\text { converges. }}\end{array}$$

True or False? In Exercises $83-86$ , determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false.

$$\frac{d}{d x}[\arctan (\tan x)]=1$$ for all $x$ in the domain.

True or False? In Exercises 81-86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$\begin{array}{l}{\text { If } f \text { is continuous on }[0, \infty) \text { and } \int_{0}^{\infty} f(x) d x \text { diverges, then }} \\ {\lim _{x \rightarrow \infty} f(x) \neq 0}\end{array}$$

True or False? In Exercises $91-96,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$0.75=0.749999 \ldots$$

TRUE OR FALSE? In Exercises 95-97, determine whether the statement is true or false. Justify your answer.

The graph of the function given by $f(x) =\ sin(x+2\pi)$ translates the graph of $f(x) =\ sin\ x$ exactly one period to the right so that the two graphs look identical.

True or False? In Exercises $83-86$ , determine whether the statement is true or false. If it is false, explain why or give anexample that shows it is false.

$$\arcsin ^{2} x+\arccos ^{2} x=1$$

True or False? In Exercises $93-98$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$\int x\left(x^{2}+1\right) d x=\frac{1}{2} x^{2}\left(\frac{1}{3} x^{3}+x\right)+C$$

True or False? In Exercises $97-100$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$\ln \left|\cos \theta^{2}\right|=\ln \left(\cos \theta^{2}\right)$$

True or False? In Exercises $87-92,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

It is possible for a parabola to intersect its directrix.

True or False? In Exercises $49-53,$ determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $y=f(x), f$ is increasing and differentiable, and $\Delta x>0,$

then $\Delta y \geq d y .$

TRUE OR FALSE? In Exercises 77-82, determine whether the statement is true or false. Justify your answer.

$tan[(5^\circ)^2] = tan^2\ 5^\circ$

True or False? In Exercises $75-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $(-4,-5)$ is a point on a graph that is symmetric with respect to the $x$ -axis, then $(4,-5)$ is also a point on the graph.

True or False? In Exercises $75-78$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If $b^{2}-4 a c=0$ and $a \neq 0,$ then the graph of

$$y=a x^{2}+b x+c$$

has only one $x$ -intercept.

If $(-4,-5)$ is a point on a graph that is symmetric with respect to the $y$ -axis, then $(4,-5)$ is also a point on the graph.