Question 1

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

Accepted Answer

$$-2$$ miles$$/$$	ext{second}$

Question 2

Which of the following functions is a constant function?

Accepted Answer

$$f(x) = 0x + 5$$

Question 3

Given the function $$f(x) = -5 + 2x$$, what is the $$y-$$intercept?

Accepted Answer

$$-5$$

Question 4

Find the slope of the line passing through the points $$(2,1)$$ and $$(5,-4).$$

Accepted Answer

$$-5/3$$

Question 5

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 6

A function $$f(x) is $$defined as $$f(x) = x^2$ + 1. Is $$this function linear or nonlinear?

Accepted Answer

Nonlinear, because the rate of change is not constant.

Question 7

What is the domain and range of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

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

Question 8

Which of the following best describes the graph of $$f(x) = 3$$?

Accepted Answer

A horizontal line

Question 9

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

Accepted Answer

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

Question 10

A function $$f is $$increasing on the interval $$(2, \infty). $$What does this mean?

Accepted Answer

For all $$x_1$$ \u003c $$x_2 in$$ $$(2, \infty)$$, $$f(x_1$) \u003c f(x_2$)$$

Question 11

Which of the following is NOT a function?

Accepted Answer

A vertical line $$x = 2$$

Question 12

If a function $$f(x) is $$decreasing on $$(-\infty, -2) \cup (2, \infty)$$, which of the following intervals is $$f(x)$$ NOT decreasing?

Accepted Answer

$$(-2, 2)$$

Question 13

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

Accepted Answer

$$(2, 0)$$

Question 14

Which of the following best describes the graph of $$f(x) = |x|$$?

Accepted Answer

A V-shaped graph opening upwards

Question 15

Suppose $$A(x) = 100 \left[1 - \frac{x}{5}\right]$$ gives the amount of water in a tank after $$x$$ minutes. What is the average rate of change of $$A$$ from $$x=1 to$$ $$x=1.5$$?

Accepted Answer

$$-20$$ gallons per minute

Question 16

Which of the following statements about the function $$f(x) = x^2$ is true?

Accepted Answer

Its range is $$[0, \infty)$$

Question 17

If the slope $$m of a $$linear function is zero, what does its graph look like?

Accepted Answer

A horizontal line

Question 18

Which of the following is an example of a nonlinear function?

Accepted Answer

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

Question 19

A function $$f(x) is $$defined as $$f(x) = 3x - 2. $$What is the slope and what does it represent in a real-world context?

Accepted Answer

Slope is $$3$$; it represents the rate of change.

Linear and Nonlinear Functions: Key Concepts in College Algebra

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