Question 1

Which of the following best describes the range of a function $$f: A \rightarrow B$$?

Accepted Answer

The set of all possible output values that $$f$$ actually produces, a subset of $$B$$

Question 2

Given the function $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$f(g(3)) = 2 \cdot 9 + 1 = 19$$

Question 3

A function $$f(x) is $$defined graphically. Which test can you use to determine if the graph represents a function?

Accepted Answer

Vertical Line Test

Question 4

Which of the following is NOT a linear function?

Accepted Answer

$$f(x) = x^2$ + 1$$

Question 5

If a function $$f(x)$$ has a constant average rate of change, which of the following must be true?

Accepted Answer

$$f(x) is a $$linear function

Question 6

Given the population model $$P(t) = 30t + 180$$, where $$t is $$years since 2000, estimate the population in 2030.

Accepted Answer

Question 7

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

Accepted Answer

$$g(f(2)) = 2 \cdot 4 + 1 = 9$$

Question 8

Which of the following statements about the slope of a linear function is correct?

Accepted Answer

If $$m = 0$$, the function is constant

Question 9

A line passes through the point $$(3, 10)$$ and has slope $$m = 5. $$What is its equation in point-slope form?

Accepted Answer

$$y - 10 = 5(x - 3)$$

Question 10

If two lines are perpendicular, what is the relationship between their slopes $$m_1$$ and $$m_2$$?

Accepted Answer

$$m_1$$ \cdot $$m_2 = -1$

Question 11

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

Accepted Answer

$$f(2) + g(2) = 2 \cdot 2 + 1 + 2^2$ = 4 + 1 + 4 = 9$$

Question 12

Which of the following is the correct formula for the average rate of change (AROC) of a function between $$x_1$$ and $$x_2$$?

Accepted Answer

$$\frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 13

A city’s population grew from 180,000 in 2000 to 240,000 in 2020. What is the average rate of change per year?

Accepted Answer

$$\frac{240,000 - 180,000}{20} = 3,000$$

Question 14

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

Accepted Answer

$$f(2) \cdot g(2) = (2 \cdot 2 + 1) \cdot (2^2$) = 5 \cdot 4 = 20$$

Question 15

Which of the following best describes the codomain of a function?

Accepted Answer

The set of all possible output values that $$f$$ could produce, regardless of whether it actually does

Question 16

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

Accepted Answer

$$\frac{f(2)}{g(2)} = \frac{2 \cdot 2 + 1}{2^2$} = \frac{5}{4}$$

Question 17

Which of the following is the correct equation for a line parallel to $$y = 4x + 5$$ passing through $$(2, 7)$$?

Accepted Answer

$$y - 7 = 4(x - 2)$$

Question 18

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

Accepted Answer

$$f(2) - g(2) = (2 \cdot 2 + 1) - (2^2$) = 5 - 4 = 1$$

Functions and Linear Functions: Precalculus Study Notes

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