Question 1

A car is initially located 30 miles north of the Texas border and travels north at 60 miles per hour. Which of the following equations best models the car's distance from the border after $$x$$ hours?

Accepted Answer

$$f(x) = 60x + 30$$

Question 2

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

Accepted Answer

$$m = -\frac{5}{3}$$

Question 3

Which of the following is NOT a characteristic of a linear function?

Accepted Answer

It can have any number of zeros.

Question 4

A function $$f is $$defined as $$f(x) = 7. $$What type of function is this, and what is its rate of change?

Accepted Answer

Constant function; rate of change is $$0$$

Question 5

Which of the following best describes the slope of a vertical line?

Accepted Answer

The slope is undefined.

Question 6

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

Accepted Answer

The function is nonlinear and its graph is not a straight line.

Question 7

If a function $$f is $$increasing on an interval $$I$$, which of the following must be true for any $$x_1$$ \u003c $$x_2 in$$ $$I$$?

Accepted Answer

$$f(x_1$) \u003c f(x_2$)$$

Question 8

A line has the equation $$y = -\frac{1}{2}x + 3. $$What does the slope indicate about the line?

Accepted Answer

The line falls $$\frac{1}{2}$$ unit for every unit increase in $$x.$$

Question 9

Which of the following functions is NOT linear?

Accepted Answer

$$f(x) = x^2$

Question 10

A company’s profit $$P (in $$dollars) after selling $$x$$ units is given by $$P(x) = 15x - 200. $$What is the meaning of the slope in this context?

Accepted Answer

The company makes $15 for each unit sold.

Question 11

Which of the following intervals describes where the function $$f(x) = 4x - \frac{1}{3}x^3$ is increasing?

Accepted Answer

$$(-2, 2)$$

Question 12

Which of the following best describes a function that is decreasing on an interval?

Accepted Answer

For any $$x_1  f$$($$x_2$$)$$

Question 13

Which of the following is a zero of the function $$f(x) = 2x - 6$$?

Accepted Answer

$$x = 3$$

Question 14

A function $$f is $$defined by $$f(x) = |x|. $$Which of the following statements is true?

Accepted Answer

The function is nonlinear and has a V-shaped graph.

Question 15

If the slope of a line is $$0$$, which of the following is true about the line?

Accepted Answer

The line is horizontal.

Question 16

Which of the following real-world scenarios is best modeled by a linear function?

Accepted Answer

The cost of buying $$x$$ gallons of gasoline at a fixed price per gallon.

Question 17

Given the function $$f(x) = \sqrt{x}$$, which of the following is true?

Accepted Answer

The function is nonlinear and increases as $$x$$ increases.

Question 18

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 19

Which of the following statements about nonlinear functions is correct?

Accepted Answer

They can have any number of zeros.

Types of Functions and Their Rates of Change: College Algebra Study Guide

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