Question 1

Which of the following is the correct domain for the function $$f(x) = \frac{3}{x^2$ - 2x}$$?

Accepted Answer

$$x 
eq 0, x 
eq 2$$

Question 2

Given $$g(x) = x^3$ - 4$$, which of the following statements is true?

Accepted Answer

$$g(x) is a $$one-to-one function.

Question 3

What is the equation of a circle with diameter endpoints at $$(1,2)$$ and $$(5,2)$$?

Accepted Answer

$$(x - 3)^2$ + (y - 2)^2$ = 4$$

Question 4

Find the $$y-$$intercept of the function $$y = -\sqrt{x^3$ + 1}.$$

Accepted Answer

$$(0, -1)$$

Question 5

A line has a slope of $$-\frac{5}{4}$$ and passes through the point $$(1,5). $$What is its equation in point-slope form?

Accepted Answer

$$y - 5 = -\frac{5}{4}(x - 1)$$

Question 6

Let $$f(x) = \frac{3}{x^2$ - 2x}$$ and $$g(x) = \frac{2}{x}. $$What is $$(f + g)(x)$$?

Accepted Answer

$$\frac{3}{x^2$ - 2x} + \frac{2}{x}$$

Question 7

Given $$f(x) = \frac{3}{x^2$ - 2x}$$ and $$g(x) = \frac{2}{x}$$, what is the domain of $$(g - f)(x)$$?

Accepted Answer

$$x 
eq 0, x 
eq 2$$

Question 8

A line passes through $$(-2,1)$$ and is parallel to the line through $$(-1,4)$$ and $$(3,3). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -\frac{1}{4}x + \frac{1}{2}$$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

For $$f(x) = \frac{3}{x^2$ - 2x}$$, what is the average rate of change from $$x = 3 to$$ $$x = 6$$?

Accepted Answer

$$\frac{f(6) - f(3)}{6 - 3}$$

Question 12

Which of the following best describes the transformation of $$f(x) = 2\sqrt[3]{x + 2} - 2$$ compared to $$y = \sqrt[3]{x}$$?

Accepted Answer

Shift left 2 units, stretch vertically by 2, shift down 2 units

Question 13

Given the piecewise function $$f(x) = \begin{cases} 2x + 1, & x \leq 2 \ 3, & x \u003e 2 \end{cases}$$, which of the following is true?

Accepted Answer

$$f(x) is $$not one-to-one.

Question 14

Which of the following is the correct method to verify algebraically that $$g(x) = x^3$ - 4 is $$one-to-one?

Accepted Answer

Show that $$g(a) = g(b)$$ implies $$a = b.$$

Question 15

If $$f(x) = -\sqrt{x^3$ + 1}$$, which of the following points lies on its graph?

Accepted Answer

$$(0, -1)$$

Question 16

Which of the following intervals describes where the function $$f(x) = 2x + 1 ($$for $$x \leq 2) is $$increasing?

Accepted Answer

$$(-\infty, 2]$$

Question 17

Given $$g(x) = x^3$ - 4$$, what is the $$x-$$intercept of the function?

Accepted Answer

$$(\sqrt[3]{4}, 0)$$

Question 18

Which of the following best describes the graph of $$f(x) = -\sqrt{x^3$ + 1}$$?

Accepted Answer

It is defined for $$x \geq -1$$ and is always non-positive.

Precalculus Study Guide: Functions, Graphs, and Equations

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