Q: Which of the following is the correct description of the end behavior of $$f(x) = -x^2$?

As $$x \to \pm \infty$$, $$f(x) \to -\infty.$$

Question 1

Which of the following describes the effect of the transformation $$g(x) = f(x - 3) + 2 on $$the parent function $$f(x)$$?

Accepted Answer

Shift the graph 3 units right and 2 units up.

Question 2

Given $$f(x) = x^2$ and g(x) = 2x + 1$, what is the domain of the function h(x) = f(g(x$$))$$?

Accepted Answer

All real numbers $$x$$

Question 3

Suppose $$f(x) = \sqrt{x}$$ and $$g(x) = x - 4. $$What is the domain of the function $$h(x) = f(g(x))$$?

Accepted Answer

All real numbers $$x$$ such that $$x \geq 4$$

Question 4

Which of the following functions is NOT one-to-one?

Accepted Answer

$$f(x) = x^2$

Question 5

Given $$f(x) = x - 400$$ and $$g(x) = 0.75x$$, which composition represents the price after a 25% discount and then a $400 rebate?

Accepted Answer

$$f \circ g(x) = 0.75x - 400$$

Question 6

Find the inverse of the function $$f(x) = \frac{x - 2}{x + 2}.$$

Accepted Answer

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

Question 7

A quadratic function $$f(x) = ax^2$ + bx + c$$ opens downward. Which statement is true about its maximum or minimum?

Accepted Answer

It has a maximum at the vertex.

Question 8

Given $$f(x) = -2x^2$ + 8x - 3$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, 5)$$

Question 9

A rectangular plot of land is to be enclosed on three sides (the fourth side is a river) with 700 feet of fencing. If $$x is $$the width perpendicular to the river, what is the function for the area $$A(x)$$?

Accepted Answer

$$A(x) = x \cdot (700 - 2x)$$

Question 10

For the function $$A(x) = x(700 - 2x)$$, what value of $$x$$ gives the maximum area?

Accepted Answer

$$x = 175$$

Question 11

Which of the following is the correct process to verify that two functions $$f$$ and $$g$$ are inverses?

Accepted Answer

Show that $$f(g(x)) = x$$ and $$g(f(x)) = x$$ for all $$x in $$the domain.

Question 12

If $$f(x) = \sqrt[3]{x}$$, what is the effect of the transformation $$g(x) = -\sqrt[3]{x + 2}$$?

Accepted Answer

Reflection over the $$x-$$axis and shift 2 units left.

Question 13

Which of the following is the correct formula for the $$x-$$coordinate of the vertex of a quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$x = -\frac{b}{2a}$$

Question 14

If $$f(x) = x^2$ and g(x) = x + 1$, what is f$$ \circ g (2)$$?

Accepted Answer

$$9$$

Question 15

Which of the following statements about the graph of $$f(x) = -x^2$ is true?

Accepted Answer

The graph opens downward and has a maximum at the vertex.

Question 16

A company models its profit with $$P(x) = -5x^2$ + 200x - 1000$$, where $$x is $$the number of units sold. What is the maximum profit, and at how many units is it achieved?

Accepted Answer

Question 17

If $$f(x) = 2x$$ and $$g(x) = x^2$, what is (f + g)(3$$)$$?

Accepted Answer

$$15$$

Question 18

Which of the following is the correct description of the end behavior of $$f(x) = -x^2$?

Accepted Answer

As $$x 	o \pm \infty$$, $$f(x) 	o -\infty.$$

College Algebra Unit 3 Review: Functions and Quadratic Functions

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