Question 1

Which of the following best describes the graph of a linear function $$f(x) = mx + b$$ when $$m \u003c 0$$?

Accepted Answer

The graph is a straight line that decreases as $$x$$ increases.

Question 2

Given the linear function $$y = 3x + 1$$, what is the slope and what does it indicate about the function?

Accepted Answer

Slope is $$3$$; the function is increasing.

Question 3

A chemical reaction's temperature is modeled by $$T(t) = -2t + 100$$, where $$T is $$temperature in degrees Celsius and $$t is $$time in minutes. What does the slope represent in this context?

Accepted Answer

The temperature decreases by $$2$$ degrees per minute.

Question 4

Which of the following equations represents a linear function with a zero slope?

Accepted Answer

$$y = 0x + 7$$

Question 5

If a linear function passes through the points $$(1, 4)$$ and $$(3, 8)$$, what is its slope?

Accepted Answer

$$m = 2$$

Question 6

A taxi company charges a flat fee of $$\3$ plus $$\$$2$$ per mile. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 2m + 3$$

Question 7

Given the function $$f(x) = -4x + 7$$, what is the $$y-$$intercept?

Accepted Answer

$$7$$

Question 8

Which of the following best describes the domain of any linear function $$f(x) = mx + b$$?

Accepted Answer

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

Question 9

A medical researcher records a patient's heart rate every hour. The data fits the function $$H(t) = 80 - 5t$$, where $$H is $$heart rate and $$t is $$hours. What is the heart rate after $$3$$ hours?

Accepted Answer

$$65$$

Question 10

Which of the following statements is true about the graph of $$y = mx + b if$$ $$m = 0$$?

Accepted Answer

The graph is a horizontal line.

Question 11

Given the points $$(2, 5)$$ and $$(6, 13)$$, what is the equation of the linear function passing through these points?

Accepted Answer

$$y = 2x + 1$$

Question 12

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = 15x - 40$$, where $$x is $$the number of units sold (in thousands). What is the break-even point?

Accepted Answer

$$x = 2.67$$

Question 13

Which of the following is NOT a linear function?

Accepted Answer

$$y = x^2$ + 1$$

Question 14

If the graph of a function is a straight line that passes through the origin and has a negative slope, which equation could represent it?

Accepted Answer

$$y = -2x$$

Question 15

A car rental company charges $$\25$ per day plus a one-time fee of $$\$$50. $$Which equation models the total cost $$C$$ for $$d$$ days?

Accepted Answer

$$C = 25d + 50$$

Question 16

Given the linear function $$f(x) = \frac{1}{2}x - 3$$, what is the range of this function?

Accepted Answer

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

Question 17

If a function is constant over its domain, what is its slope?

Accepted Answer

$$0$$

Question 18

A line passes through $$(0, 2)$$ and $$(4, 10). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 2x + 2$$

Question 19

Which of the following best describes the range of a linear function $$f(x) = mx + b$$?

Accepted Answer

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

3.1 Real Numbers and Linear Functions: Precalculus Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards