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Find the amplitude, the period, any vertical translation, and any phase shift of the graph of each function. See Examples 1–5.
$$y=-\frac{1}{2} \sin \left(\frac{1}{2} x+\pi\right)$$

Find the amplitude, the period, any vertical translation, and any phase shift of the graph of each function. See Examples 1–5. $$y=-\frac{1}{2} \sin \left(\frac{1}{2} x+\pi\right)$$

Precalculus

The Circular Functions and Their Graphs

Translations of the Graphs of the sine…

Questions asked

INSTANT ANSWER

select all of the following graphs which are one-to-one functions.

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INSTANT ANSWER

Select all of the following graphs which represent \( \boldsymbol{y} \) as a function of \( \boldsymbol{x} \).

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INSTANT ANSWER

Given the function \( f(x)=-8+7 x^{2} \), calculate the following values: \[ \begin{array}{l} f(a)=\square \\ f(a+h)=\square \\ \frac{f(a+h)-f(a)}{h}=\square \end{array} \]

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INSTANT ANSWER

For the function \( f(x)=-5 x+6 \), evaluate and simplify the difference quotient. \( \square \)

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INSTANT ANSWER

For the function \( f(x)=-6 x^{2}+3 x \), evaluate and fully simplify each of the following. \[ f(x+h)= \] \( \square \) \[ \frac{f(x+h)-f(x)}{h}= \] \( \square \)

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INSTANT ANSWER

For the function \( f(x)=5 x^{2}-4 x \), evaluate and simplify. \[ \frac{f(x+h)-f(x)}{h}= \]

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INSTANT ANSWER

Given the function \( f(x)=5 x+6 \), evaluate and simplify the expressions below. See special instructions on how to enter your answers. \[ f(a)= \] \( \square \) \[ \begin{array}{l} f(a+h)= \\ \frac{f(a+h)-f(a)}{h}= \end{array} \] \( \square \) \( \square \) Instructions: Simplify answers as much as possible. Expressions such as \( 4(x+2) \) and \( (x+5)^{2} \) should be expanded. Also collect like terms, so \( 3 x+x \) should be written as \( 4 x \).

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INSTANT ANSWER

Match each function name with its equation. \( \square \) \( y=x^{3} \) \( \square \) \( y=x^{2} \) \( \square \) \( y=\sqrt{x} \) \( \square \) \( y=x \) \( \square \) \( y=\sqrt[3]{x} \) \( \boxed{-\vee} y=\frac{1}{x} \) \( \square \) \( y=|x| \) \( \square \) \( y=\frac{1}{x^{2}} \) a. Quadratic b. Cubic c. Absolute Value d. Cube root e. Reciprocal f. Reciprocal Squared g. Linear h. Square Root

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INSTANT ANSWER

Suppose \( f(x)=-3 x^{2}-9 x+1 \). Compute the following: A.) \( f(-5)+f(2)= \) \( \square \) B.) \( f(-5)-f(2)= \) \( \square \)

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INSTANT ANSWER

Given the function \( f(x)=8 x^{2}-6 x+5 \). Calculate the following values: \[ \begin{array}{l} f(-2)=\square \\ f(-1)=\square \\ f(0)=\square \\ f(1)=\square \\ f(2)=\square \end{array} \]

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