Question 1

A car's distance from the Texas border is modeled by $$f(x) = 60x + 30$$, where $$x is $$time in hours. What does the number 30 represent in this context?

Accepted Answer

The car's initial distance from the Texas border in miles.

Question 2

Given the function $$f(x) = 3x + 7$$, what is the zero of the function?

Accepted Answer

$$x = -\frac{7}{3}$$

Question 3

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

Accepted Answer

It can increase and decrease on the same interval.

Question 4

Find the slope of the line passing through the points $$(-2, 3)$$ and $$(1, -2). $$What does the sign of the slope indicate?

Accepted Answer

$$m = -\frac{5}{3}$$; the line is decreasing.

Question 5

Which equation represents the average rate of change of a function $$f(x)$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 6

Let $$f(x) = 2x^2$. Find the average rate of change from x = 1$ to x = 3$.

Accepted Answer

$$8$$

Question 7

Which of the following functions is NOT linear?

Accepted Answer

$$f(x) = x^2$ + 1$$

Question 8

The difference quotient for a function $$f(x) is $$given by $$\frac{f(x+h) - f(x)}{h}. $$What is the simplified difference quotient for $$f(x) = -2x + 5$$?

Accepted Answer

$$-2$$

Question 9

A water tank contains 100 gallons. Water drains at a rate of 5 gallons per minute, modeled by $$G(x) = 100 - 5x. $$What does the slope of this function represent?

Accepted Answer

The rate at which water is drained from the tank.

Question 10

If $$f(1) = 12$$ and $$f(4) = -3$$, what is the average rate of change of $$f$$ from $$x = 1 to$$ $$x = 4$$?

Accepted Answer

$$-5$$

Question 11

Which of the following best describes a function that is increasing on an interval $$I$$?

Accepted Answer

For any $$x_1$$ \u003c $$x_2 in$$ $$I$$, $$f(x_1$) \u003c f(x_2$).$$

Question 12

In the context of rock music sales, if the function $$y = f(x)$$ decreases from 36% to 24% between 1990 and 2001, what does this indicate about the function on this interval?

Accepted Answer

The function is decreasing on this interval.

Question 13

Which of the following statements about the graph of a linear function is TRUE?

Accepted Answer

The graph is always a straight line.

Question 14

Given the function $$f(x) = 3x - 2$$, what is $$f(x + h)$$?

Accepted Answer

$$3(x + h) - 2$$

Question 15

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 16

Which of the following is a zero of the function $$f(x) = 1.5x + 3$$?

Accepted Answer

$$x = -2$$

Question 17

Which of the following is a characteristic of a nonlinear function?

Accepted Answer

It can increase and decrease on its domain.

Question 18

If $$f(x) = \sqrt{x}$$, which of the following statements is TRUE about its graph?

Accepted Answer

It is only defined for $$x \geq 0.$$

Question 19

A company spent $$95$$ billion on advertising in $$1985$$ and $$270$$ billion in $$2005. $$What is the slope of the line passing through these points, and what does it represent?

Accepted Answer

$$8.75$$; the average annual increase in advertising spending.

Question 20

Given the piecewise graph shown (last image), on which interval is the function decreasing?

Accepted Answer

$$-5 \u003c x \u003c 1$$

Types of Functions and Their Rate of Change

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