Question 1

Which of the following equations defines $$y as a $$function of $$x$$?

Accepted Answer

$$y = x^2$ - 2x$$

Question 2

Given $$f(x) = -x^2$ + 2x - 3$$, what is $$f(-1)$$?

Accepted Answer

$$-6$$

Question 3

Find the domain of $$f(x) = \frac{2}{x^2$}.$$

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 4

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

Accepted Answer

$$2x^2 + 2x - 3$

Question 5

Which of the following graphs is NOT a function?

Accepted Answer

A vertical ellipse centered at the origin

Question 6

Given $$f(x) = \frac{2x}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 7

Suppose $$f(x) = x^2$ - 2x + 1. Is$$ $$f$$ even, odd, or neither?

Accepted Answer

Neither

Question 8

Find the average rate of change of $$f(x) = x^2$ + 3x^2$ from x = 1$ to x = 4$.

Accepted Answer

$$-4$$

Question 9

Given the piecewise function $$h(x) = \begin{cases} x + 4 & x \geq -4 \ -x - 4 & x \u003c -4 \end{cases}$$, what is $$h(-5)$$?

Accepted Answer

$$1$$

Question 10

Which transformation sequence produces $$f(x) = -(x-3)^2$ - 2$$ from $$y = x^2$?

Accepted Answer

Shift right 3 units, reflect about the x-axis, shift down 2 units

Question 11

If $$f(x) = \sqrt{x}$$, what is the graph of $$f(x) = \frac{1}{2}\sqrt{x-2}$$?

Accepted Answer

The graph of $$\sqrt{x}$$ shifted right 2 units and vertically compressed by $$\frac{1}{2}$$

Question 12

Given $$f(x) = |x|$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$f(x) + g(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 13

Which of the following is the correct definition for the piecewise function graphed as $$f(x) = \begin{cases} 0 & x  1 \end{cases}$$?

Accepted Answer

$$f(x) = \begin{cases} 0 & x  1 \end{cases}$$

Question 14

Suppose the x-intercepts of $$y = f(x)$$ are 2 and -4. What are the x-intercepts of $$y = 2f(x)$$?

Accepted Answer

2 and -4

Question 15

For $$f(x) = \frac{5}{\sqrt{x+4}}$$, what is the domain?

Accepted Answer

$$(-4, \infty)$$

Question 16

If $$f(x) = 2x - 3$$ and $$g(x) = 2x^2$, what is $$\left(\frac{f}{g}\right)(3)$$?

Accepted Answer

$$\frac{1}{6}$$

Question 17

Which of the following best describes the intervals where the function $$f(x) is $$increasing, given the graph increases on $$(-5, -4)$$, decreases on $$(1, 4)$$, and is continuous on $$(-4, 1)$$?

Accepted Answer

Increasing on $$(-5, -4)$$

Question 18

Given $$f(x) = 2x^2$ + 3x - 5$$, which of the following is the correct range for $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Precalculus Study Guide: Functions, Graphs, and Transformations

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