Question 1

Which of the following relations is NOT a function?

Accepted Answer

A relation where the graph fails the vertical line test.

Question 2

Given the function $$f(x) = x^2$ - 4$$, what is the domain of $$f(x)$$?

Accepted Answer

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

Question 3

If $$g(x) = \sqrt{x-2}$$, what is the range of $$g(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 4

Which transformation is applied to $$f(x) = x^2$ to obtain h(x$$) = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units, up 2 units

Question 5

Given $$f(x) = \frac{3}{x}$$ and $$g(x) = x-5$$, what is $$f(g(x))$$?

Accepted Answer

$$\frac{3}{x-5}$$

Question 6

What is the $$y-$$intercept of the function $$f(x) if$$ $$f(0) = 2$$?

Accepted Answer

$$(0,2)$$

Question 7

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

Accepted Answer

$$9$$

Question 8

Which of the following intervals represents where the function $$f(x) is $$increasing based on the graph provided?

Accepted Answer

$$(-\infty, -2) \cup (2, 7)$$

Question 9

Given the data on wine consumption and heart disease, what is the best interpretation of the negative slope in the regression line?

Accepted Answer

As wine consumption increases, deaths from heart disease decrease.

Question 10

If $$h(x) = 1.4x + 13.2$$ models the percentage of health care spending, what does the slope $$1.4$$ represent in this context?

Accepted Answer

The percentage increase in health care spending per year.

Question 11

Which of the following is the correct inverse of $$f(x) = 2x + 1$$?

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

$$(x+3)^2$$

Question 14

Which of the following best describes the transformation from $$f(x) = \sqrt{x} to$$ $$g(x) = \sqrt{x+2} - 3$$?

Accepted Answer

Shift left 2 units, down 3 units

Question 15

If $$f(x) = x^2$ and f$$^{-1}$$(x) is $$its inverse, what is the domain of $$f^{-1}(x$$)$$?

Accepted Answer

$$[0, \infty)$$

Question 16

Given the function $$f(x) = \frac{1}{x-1}$$, for which value of $$x is$$ $$f(x)$$ undefined?

Accepted Answer

$$x = 1$$

Question 17

If $$y = -0.25x + 22.2$$ models the percentage of food spending, what does the negative slope indicate?

Accepted Answer

Food spending as a percentage of total spending is decreasing over time.

Question 18

Which of the following is the correct composition $$f(g(x)) if$$ $$f(x) = x^2$ and g(x) = 2x-1$?

Accepted Answer

$$(2x-1)^2$$

Question 19

Given the function $$f(x) = \sqrt{x-4}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$[4, \infty)$$

Question 20

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

Accepted Answer

$$9$$

Precalculus Review Worksheet: Functions, Transformations, Domain & Range, and Data Analysis

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