Question 1

Given the graph of the price $$p(t) of $$landscape rock in dollars as a function of tons $$t$$, why is it reasonable for the graph to pass through the origin?

Accepted Answer

Because buying zero tons of rock should cost zero dollars.

Question 2

Using the graph provided, what is the slope of the line representing the price of landscape rock, and what does it represent?

Accepted Answer

The slope is $$25$$, representing $$25$$ dollars per ton.

Question 3

Which of the following equations best models the price $$p(t) of$$ $$t$$ tons of landscape rock, based on the graph?

Accepted Answer

$$p(t) = 25t$$

Question 4

What is the relevant domain for the function $$p(t) if $$there is a 30-ton limit on the amount of landscape rock that can be purchased?

Accepted Answer

$$[0, 30]$$

Question 5

Which of the following is NOT a linear function?

Accepted Answer

$$f(x) = x^2$

Question 6

Given the function $$f(x) = \frac{3}{2}x + 3$$, what is the $$y-$$intercept?

Accepted Answer

$$3$$

Question 7

Which of the following best describes the slope of the line $$y = -2x + 5$$?

Accepted Answer

Negative slope; the function is decreasing.

Question 8

Which of the following functions is increasing for all $$x in $$its domain?

Accepted Answer

$$f(x) = x^3$

Question 9

The height in feet of a firework shell is modeled by $$H(t) = -16t^2$ + 256t. $$What is the relevant domain for $$t if$$ $$H(t)$$ represents the height above ground?

Accepted Answer

$$[0, 16]$$

Question 10

For the function $$H(t) = -16t^2$ + 256t$$, over which interval is the height of the firework increasing?

Accepted Answer

$$[0, 8]$$

Question 11

What is the average rate of change of $$f(x) = x^2$ from x = 1$ to x = 4$?

Accepted Answer

$$5$$

Question 12

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

Accepted Answer

It decreases for $$x  0.$$

Question 13

If the price of landscape rock is given by $$p(t) = 25t$$, what is the range if the maximum purchase is 30 tons?

Accepted Answer

$$[0, 750]$$

Question 14

Which of the following is a nonlinear function?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 15

A company charges $$p(t) = 25t$$ dollars for $$t$$ tons of rock. If a customer has a budget of $$100$$, what is the maximum whole number of tons they can purchase?

Accepted Answer

$$4$$

Question 16

For the function $$H(t) = -16t^2$ + 256t$$, what is the maximum height reached by the firework shell?

Accepted Answer

$$1024$$ feet

Question 17

Which of the following intervals describes where the function $$f(x) = x^2$ is decreasing?

Accepted Answer

$$(-\infty, 0)$$

Question 18

If $$f(x) = 3x + 2$$ and $$g(x) = x^2$, which function has a constant rate of change?

Accepted Answer

$$f(x)$$ only

Question 19

Suppose $$f(x) is a $$linear function with a positive slope. Which statement is true?

Accepted Answer

$$f(x) is $$increasing for all $$x.$$

Question 20

If the average rate of change of a function $$f(x)$$ from $$x = 2 to$$ $$x = 5 is$$ $$10$$, which of the following must be true?

Accepted Answer

$$\frac{f(5) - f(2)}{5 - 2} = 10$$

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

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