Q: For the function $$f(x) = 34x + 4$$, what is the average rate of change between $$x = 1$$ and $$x = 3$$?

$$\dfrac{f(3) - f(1)}{3 - 1} = \dfrac{(34 \times 3 + 4) - (34 \times 1 + 4)}{2} = 34$$

Question 1

Which of the following equations represents a linear function?

Accepted Answer

$$f(x) = 5x - 7$$

Question 2

Given the linear function $$f(x) = -3x + 8$$, what is the slope and y-intercept?

Accepted Answer

Slope: $$-3$$, y-intercept: $$8$$

Question 3

A truck rental company charges $$32 plus 0.05 $$per mile. Which equation models the total cost $$C(x)$$ for $$x$$ miles driven?

Accepted Answer

$$C(x) = 0.05x + 32$$

Question 4

Given two points $$A(3, 4)$$ and $$B(6, 2)$$, what is the slope of the line passing through them?

Accepted Answer

$$m = \dfrac{2 - 4}{6 - 3} = -\dfrac{2}{3}$$

Question 5

Suppose the cost to tow a car is modeled by $$C(x) = 1.5x + 95$$, where $$x is $$the number of miles towed. If you have $131, what is the maximum number of miles you can be towed?

Accepted Answer

$$x = \dfrac{131 - 95}{1.5} = 24$$

Question 6

Given the supply and demand functions $$S(p) = -200 + 40p$$ and $$D(p) = 1150 - 50p$$, what is the equilibrium price?

Accepted Answer

$$p = 15$$

Question 7

For the function $$f(x) = 34x + 4$$, what is the average rate of change between $$x = 1$$ and $$x = 3$$?

Accepted Answer

$$\dfrac{f(3) - f(1)}{3 - 1} = \dfrac{(34 	imes 3 + 4) - (34 	imes 1 + 4)}{2} = 34$$

Question 8

A linear function is increasing when:

Accepted Answer

$$m \u003e 0$$

Question 9

Given the table below, determine if the function is linear and, if so, find the slope.

x: 1, 2, 3, 4, 5
y: 7, 12, 17, 22, 27

Accepted Answer

The function is linear with slope $$m = 5$$

Question 10

Given the table below, determine if the function is linear and, if so, find the slope.

x: 0, 1, 2, 3, 4
y: -12, -6, -4, -3, -5

Accepted Answer

The function is nonlinear

Question 11

Suppose $$f(x) is a $$linear function and $$f(40) = 70$$, $$f(96) = 119. $$What is the equation of $$f(x)$$?

Accepted Answer

$$f(x) = \dfrac{119 - 70}{96 - 40}(x - 40) + 70$$

Question 12

If the quantity demanded is greater than the quantity supplied for T-shirts at a concert, what will eventually happen to the price?

Accepted Answer

The price will increase.

Question 13

Given the graph of $$y = f(x)$$ passing through $$(-40, 0)$$, $$(40, 70)$$, and $$(96, 119)$$, what is the value of $$x$$ when $$f(x) = 0$$?

Accepted Answer

$$x = -40$$

Question 14

Suppose $$f(x)$$ and $$g(x)$$ are linear functions whose graphs intersect at $$(-1, 3). $$What does this point represent?

Accepted Answer

The solution to $$f(x) = g(x)$$

Question 15

If $$C(x) = 1.5x + 95$$ models the cost to tow a car, and the cost is $$191$$, how many miles was the car towed?

Accepted Answer

$$x = \dfrac{191 - 95}{1.5} = 64$$

Question 16

Which of the following best describes the domain of the cost function $$C(x) = 1.5x + 95$$ for towing a car?

Accepted Answer

All real numbers $$x \geq 0$$

Question 17

If a linear function is constant, what is the value of its slope?

Accepted Answer

$$m = 0$$

Linear Functions and Their Properties: Precalculus Study Guidance

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