Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

The intercepts of the equation $9 x^{2}+4 y=36$ are $(p p .159-160)$

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

Is the expression $4 x^{3}-3.6 x^{2}-\sqrt{2}$ a polynomial? If so, what is its degree? (pp. 39-47)

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

To graph $y=x^{2}-4,$ you would shift the graph of $y=x^{2}$______a distance of_____units.

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

Use a graphing utility to approximate (rounded to two decimal places) the local maximum value and local minimum value of $f(x)=x^{3}-2 x^{2}-4 x+5,$ for $-3<x<3 .

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

The $x$ -intercepts of the graph of a function $y=f(x)$ are the real solutions of the equation $f(x)=0$

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

If $g(5)=0,$ what point is on the graph of $g ?$ What is the corresponding $x$ -intercept of the graph of $g ?

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

The graph of every polynomial function is both_____and_____.

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

If $r$ is a real zero of even multiplicity of a function $f,$ then the_____graph of $f$_____units.

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The graphs of power functions of the form $f(x)=x^{n},$ where $n$ is an even integer, always contain the points_____,_____and_____.

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

If $r$ is a solution to the equation $f(x)=0,$ name three additional statements that can be made about $f$ and $r$ assuming $f$ is a polynomial function.

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called______.

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

The graph of the function $f(x)=3 x^{4}-x^{3}+5 x^{2}-2 x-7 $will behave like the graph of_____for large values of $|x|$.

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

$$\text { If } f(x)=-2 x^{5}+x^{3}-5 x^{2}+7, \text { then } \lim _{1 x} f(x)=$$_____$$\text { and } \lim f(x)=$$_____.

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Answers are given at the end of these exercises If you get a wrong answer read the pages listed in red.

Explain what the notation $\lim _{x \rightarrow \infty} f(x)=-\infty$ means.

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$f(x)=4 x+x^{3}$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$f(x)=5 x^{2}+4 x^{4}$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$g(x)=\frac{1-x^{2}}{2}$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$h(x)=3-\frac{1}{2} x$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$f(x)=1-\frac{1}{x}$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$f(x)=x(x-1)$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$g(x)=x^{3 / 2}-x^{2}+2$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$h(x)=\sqrt{x}(\sqrt{x}-1)$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$F(x)=5 x^{4}-\pi x^{3}+\frac{1}{2}$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$F(x)=\frac{x^{2}-5}{x^{3}}$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$G(x)=2(x-1)^{2}\left(x^{2}+1\right)$$

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Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

$$G(x)=-3 x^{2}(x+2)^{3}$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=(x+1)^{4}$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=(x-2)^{5}$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=x^{5}-3$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=x^{4}+2$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=\frac{1}{2} x^{4}$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=3 x^{5}$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=-x^{5}$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=-x^{4}$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=(x-1)^{5}+2$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=(x+2)^{4}-3$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=2(x+1)^{4}+1$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=\frac{1}{2}(x-1)^{5}-2$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=4-(x-2)^{5}$$

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Use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.

$$f(x)=3-(x+2)^{4}$$

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Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros: $-1,1,3 ;$ degree 3

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Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros: $-2,2,3 ;$ degree 3

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Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros: $-3,0,4 ;$ degree 3

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Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros: $-4,0,2 ;$ degree 3

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Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros: $-4,-1,2,3 ;$ degree 4

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Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros: $-3,-1,2,5 ;$ degree 4

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Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros: -1, multiplicity 1; 3, multiplicity 2; degree 3

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Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros: $-2,$ multiplicity $2 ; 4,$ multiplicity $1 ;$ degree 3

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=3(x-7)(x+3)^{2}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=4(x+4)(x+3)^{3}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=4\left(x^{2}+1\right)(x-2)^{3}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=2(x-3)\left(x^{2}+4\right)^{3}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=-2\left(x+\frac{1}{2}\right)^{2}(x+4)^{3}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=\left(x-\frac{1}{3}\right)^{2}(x-1)^{3}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=(x-5)^{3}(x+4)^{2}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=(x+\sqrt{3})^{2}(x-2)^{4}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=3\left(x^{2}+8\right)\left(x^{2}+9\right)^{2}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=-2\left(x^{2}+3\right)^{3}$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=-2 x^{2}\left(x^{2}-2\right)$$

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For each polynomial function:

(a) List each real zero and its multiplicity.

(b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.

(c) Determine the behavior of the graph near each $x$ -intercept (zero).

(d) Determine the maximum number of turning points on the graph.

(e) Determine the end behavior; that is, find the power function that the graph of fresembles for large values of $|x|$.

$$f(x)=4 x\left(x^{2}-3\right)$$

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Identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that could not, say why not.

(THE GRAPH CANNOT COPY)

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(THE GRAPH CANNOT COPY)

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(THE GRAPH CANNOT COPY)

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(THE GRAPH CANNOT COPY)

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Construct a polynomial function that might have the given graph. (More than one answer may be possible.)

(THE GRAPH CANNOT COPY)

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(THE GRAPH CANNOT COPY)

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(THE GRAPH CANNOT COPY)

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(THE GRAPH CANNOT COPY)

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=x^{2}(x-3)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=x(x+2)^{2}$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=(x+4)(x-2)^{2}$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=(x-1)(x+3)^{2}$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=-2(x+2)(x-2)^{3}$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=-\frac{1}{2}(x+4)(x-1)^{3}$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=(x+1)(x-2)(x+4)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=(x-1)(x+4)(x-3)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=x^{2}(x-2)(x+2)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=x^{2}(x-3)(x+4)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=(x+1)^{2}(x-2)^{2}$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=(x+1)^{3}(x-3)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=x^{2}(x-3)(x+1)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=x^{2}(x-3)(x-1)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=(x+2)^{2}(x-4)^{2}$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=(x-2)^{2}(x+2)(x+4)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=x^{2}(x-2)\left(x^{2}+3\right)$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 .

$$f(x)=x^{2}\left(x^{2}+1\right)(x+4)$$

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Analyze each polynomial function $f$ by following Steps 1 through 8 on page 336.

$$f(x)=x^{3}+0.2 x^{2}-1.5876 x-0.31752$$

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Analyze each polynomial function $f$ by following Steps 1 through 8 on page

$$f(x)=x^{3}-0.8 x^{2}-4.6656 x+3.73248$$

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Analyze each polynomial function $f$ by following Steps 1 through 8 on page

$$f(x)=x^{3}+2.56 x^{2}-3.31 x+0.89$$

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Analyze each polynomial function $f$ by following Steps 1 through 8 on page

$$f(x)=x^{3}-2.91 x^{2}-7.668 x-3.8151$$

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Analyze each polynomial function $f$ by following Steps 1 through 8 on page 336.

$$f(x)=x^{4}-2.5 x^{2}+0.5625$$

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Analyze each polynomial function $f$ by following Steps 1 through 8 on page 336.

$$f(x)=x^{4}-18.5 x^{2}+50.2619$$

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Analyze each polynomial function $f$ by following Steps 1 through 8 on page 336.

$$f(x)=2 x^{4}-\pi x^{3}+\sqrt{5} x-4$$

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Analyze each polynomial function $f$ by following Steps 1 through 8 on page 336.

$$f(x)=-1.2 x^{4}+0.5 x^{2}-\sqrt{3} x+2$$

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In Problems $95-102$, analyze each polynomial function by following Steps 1 through 6 on page 333 . [Hint: You will need to first factor the polynomial].

$$f(x)=4 x-x^{3}$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 . [Hint: You will need to first factor the polynomial].

$$f(x)=x-x^{3}$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 . [Hint: You will need to first factor the polynomial].

$$f(x)=x^{3}+x^{2}-12 x$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 . [Hint: You will need to first factor the polynomial].

$$f(x)=x^{3}+2 x^{2}-8 x$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 . [Hint: You will need to first factor the polynomial].

$$f(x)=2 x^{4}+12 x^{3}-8 x^{2}-48 x$$

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Analyze each polynomial function by following Steps 1 through 6 on page 333 . [Hint: You will need to first factor the polynomial].

$$f(x)=4 x^{3}+10 x^{2}-4 x-10$$

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Construct a polynomial function $f$ with the given characteristics.

Zeros: $-3,1,4 ;$ degree $3 ; y$ -intercept: 36

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Construct a polynomial function $f$ with the given characteristics.

Zeros: $-4,-1,2 ;$ degree $3 ; y$ -intercept: 16

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Construct a polynomial function $f$ with the given characteristics.

Zeros: $-5$ (multiplicity 2 ); 2 (multiplicity 1 ): 4 (multiplicity 1 ); degree $4 ;$ contains the point $(3,128)$

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Construct a polynomial function $f$ with the given characteristics.

Zeros: $-4 \text { (multiplicity } 1) ; 0$ (multiplicity 3 ); 2 (multiplicity 1 ):

degree 5 ; contains the point $(-2,64)$

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Construct a polynomial function $f$ with the given characteristics.

$-G(x)=(x+3)^{2}(x-2)$

(a) Identify the $x$ -intercepts of the graph of $G$

(b) What are the $x$ -intercepts of the graph of $y=G(x+3) ?$

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Construct a polynomial function $f$ with the given characteristics.

$h(x)=(x+2)(x-4)^{3}$

(a) Identify the $x$ -intercepts of the graph of $h$

$\begin{array}{lllllllll}\text { (b) What } & \text { are } & \text { the } & x \text { -intercepts } & \text { of } & \text { the } & \text { graph } & \text { of }\end{array}$ $y=h(x-2) ?$

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