Quiz about Math 3 EOC Review: Inverses, Piecewise, and Absolute Value

Question 1

Which of the following is the inverse of the function below?

$$f\left(x\right)=-\frac{3}{4}x+5$$

Accepted Answer

$$f^{-1}\left(x\right)=-\frac{4}{3}x+\frac{20}{3}$$

Answer

$$f^{-1}\left(x\right)=\frac{3}{4}x-5$$

Answer

$$f^{-1}\left(x\right)=-\frac{4}{3}x+\frac{5}{3}$$

Answer

$$f^{-1}\left(x\right)=-\frac{3}{4}x-\frac{20}{3}$$

Question 2

What is the inverse of the function below with the given domain restriction?

$$f\left(x\right)=3\left(x-2\right)^2-1$$ , for all $$x\le2$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 3

Which of the following graphs shows a function and its inverse?

Accepted Answer

Question 4

What is the value of the following expression?

$$2\left[f\left(-2\right)\right]-\frac{1}{2}\left[f\left(3\right)\right]$$

Accepted Answer

1

Answer

-23

Answer

-1

Answer

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Question 5

At his job, Smitty earns a bonus of $50 for each sale that he makes up to and including the first 20 sales. After that, he makes a bonus of $80 per sale for all sales after the first 20 and up to 40. Finally, he makes $100 per sale for all sales after the first 40.

If Smitty makes 58 sales, how much bonus money, in total, will he earn?

Accepted Answer

$4,400

Answer

$3,800

Answer

$5,000

Answer

$5,800

Question 6

A portion of an absolute value function is shown. The domain of the function is all real numbers.

Which of the following statements is true of the function?

Accepted Answer

One of the intervals that the function is negative on is $$\left(4.5,\ \infty\right)$$ .

Answer

The range is $$\left(-\infty,\ 2\right]$$ .

Answer

As its x-values approach $$-\infty$$ , its y-values approach $$\infty$$ .

Answer

The function is decreasing on the interval of x-values $$\left(2,\ -\infty\right)$$ .

Question 7

What is the solution set for the equation below?

$$\left|2x-5\right|+6=3x-3$$

Accepted Answer

$$\left\{4\right\}$$

Answer

$$\left\{2.8\right\}$$

Answer

$$\left\{2.8,\ 4\right\}$$

Answer

$$\left\{\ \ \ \right\}$$

Question 8

Which of the following interval notations represents the entire solution set to the inequality below?

$$-2\left|x-8\right|+5<2$$

Accepted Answer

$$\left(-\infty,\ 6.5\right)\cup\left(9.5,\ \infty\right)$$

Answer

$$\left(9.5,\ \infty\right)$$

Answer

$$\left(6.5,\ 9.5\right)$$

Answer

$$\left(-\infty,\ \infty\right)$$

Question 9

The ideal weight of a pudding cup that is manufactured by a particular company is 113 grams. As long as the pudding cup is within 5 grams of this weight, then it gets packaged and distributed. If the pudding cup is not within 5 grams of the ideal weight, then it is sent back to the factory for reprocessing.