Question 1

Which of the following equations represents a linear function with a slope of $$-3$$ and a $$y-$$intercept of $$5$$?

Accepted Answer

$$f(x) = -3x + 5$$

Question 2

Given the points $$(2, 1)$$ and $$(3, -4)$$, what is the slope $$m of $$the line passing through them?

Accepted Answer

$$m = \frac{-4 - 1}{3 - 2} = \frac{-5}{1} = -5$$

Question 3

A function $$f(x) is $$called a constant function if:

Accepted Answer

Its slope $$m is$$ $$0$$ and its graph is a horizontal line.

Question 4

Which of the following is NOT a function?

Accepted Answer

A vertical line $$x = 2.$$

Question 5

Find the $$x-$$intercept of the line $$f(x) = 2x - 4.$$

Accepted Answer

$$(2, 0)$$

Question 6

Which of the following functions is nonlinear?

Accepted Answer

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

Question 7

Given the function $$f(x) = x^2$, what is its domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, \infty)$$

Question 8

For the function $$f(x) = \sqrt{x}$$, which of the following best describes its domain and range?

Accepted Answer

Domain: $$[0, \infty)$$, Range: $$[0, \infty)$$

Question 9

Which interval describes where the function $$f(x) is $$increasing if $$f(x) is $$shown to rise from left to right between $$x = -2$$ and $$x = 2$$?

Accepted Answer

$$(-2, 2)$$

Question 10

A car's speed is $$30$$ mph at $$t = 2$$ seconds and $$24$$ mph at $$t = 5$$ seconds. What is the average rate of change of the speed from $$t = 2 to$$ $$t = 5$$ seconds?

Accepted Answer

$$-2$$ mph$$/sec$

Question 11

Given $$f(x) = |x|$$, what is the range of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 12

Which of the following best describes the average rate of change of a function $$f(x)$$ from $$a to$$ $$b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 13

Suppose a function $$g(x) is $$decreasing on the interval $$(-\infty, -2) \cup (2, \infty). $$Which of the following is true?

Accepted Answer

The function is decreasing for $$x  2.$$

Question 14

If the graph of a function passes the vertical line test, what does this indicate?

Accepted Answer

It is a function.

Question 15

Given the function $$f(x) = x^3$, what is its range?

Accepted Answer

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

Question 16

Which of the following is the correct formula for the slope $$m of a $$line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 17

A tank contains $$100$$ gallons of water. The amount of water remaining after $$x$$ minutes is $$A(x) = 100 \left(1 - \frac{x}{5}\right). $$What is the average rate of change of $$A$$ from $$x = 1 to$$ $$x = 1.5$$?

Accepted Answer

$$-20$$ gallons/minute

Question 18

Which of the following best describes a function that is increasing on $$(2, \infty)$$ and decreasing on $$(-\infty, 2)$$?

Accepted Answer

A function with a maximum at $$x = 2$$

Question 19

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$ + 1$$, which function is linear and which is nonlinear?

Accepted Answer

$$f(x) is $$linear, $$g(x) is $$nonlinear

Linear and Nonlinear Functions: Key Concepts in College Algebra

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