Question 1

Which of the following is the general form of a linear function?

Accepted Answer

$$f(x) = mx + b$$

Question 2

Given the linear function $$f(x) = -3x + 7$$, what is the slope and y-intercept?

Accepted Answer

Slope: $$-3$$, y-intercept: $$7$$

Question 3

What is the domain of any linear function $$f(x) = mx + b$$?

Accepted Answer

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

Question 4

A company buys a computer for $$3000 and depreciates it linearly to 0$ over 3$ years. What is the linear model for the value V$ of the computer after x$ years?

Accepted Answer

$$V(x) = 3000 - 1000x$$

Question 5

Using the model $$V(x) = 3000 - 1000x$$, what is the value of the computer after $$2$$ years?

Accepted Answer

$$1000$$

Question 6

Given the supply and demand graph, what is the equilibrium price and quantity for T-shirts at the concert?

Accepted Answer

Equilibrium price: $$24$$, Equilibrium quantity: $$600$$

Question 7

If the slope $$m of a $$linear function is positive, what can you say about the function?

Accepted Answer

It is increasing over its domain.

Question 8

Suppose the average rate of change of a function is constant and equal to $$5. $$Which of the following could be the function?

Accepted Answer

$$f(x) = 5x + 2$$

Question 9

Given the table for $$y = -3x + 7$$, what is the average rate of change between $$x = -2$$ and $$x = 2$$?

Accepted Answer

$$-3$$

Question 10

If the quantity demanded is greater than the quantity supplied at a given price, what will likely happen to the price?

Accepted Answer

The price will increase.

Question 11

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

Accepted Answer

Its graph is a parabola.

Question 12

A linear function is constant if its slope is:

Accepted Answer

$$0$$

Question 13

A function $$f(x)$$ has an average rate of change that is not constant. Which of the following statements is true?

Accepted Answer

$$f(x) is $$nonlinear.

Question 14

Suppose a car depreciates by $$2000$$ per year from an initial value of $$20,000. $$What is the linear model for the car's value $$V$$ after $$x$$ years?

Accepted Answer

$$V(x) = 20000 - 2000x$$

Question 15

If $$f(x) = 4x - 5$$, what is $$f(3)$$?

Accepted Answer

$$7$$

Question 16

Which scenario best describes a real-world application of a linear function?

Accepted Answer

A cell phone plan that charges a fixed monthly fee plus a constant rate per minute.

Question 17

If $$f(x) = mx + b is $$decreasing, which of the following must be true?

Accepted Answer

$$m \u003c 0$$

Question 18

A linear function passes through the points $$(1, 4)$$ and $$(3, 8). $$What is its slope?

Accepted Answer

$$2$$

Question 19

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

Accepted Answer

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

Question 20

If the supply function is $$S(p) = 50p$$ and the demand function is $$D(p) = 1200 - 25p$$, what is the equilibrium price?

Accepted Answer

$$16$$

Study Notes: Linear Functions and Linear Models (Precalculus Chapter 3.1)

Study Guide - Practice Questions

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