5.15.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

Whenever the input of a function $f$ increases by 1, the output increases by 5. Which of these equations could define $f$ ?

The function $f$ is defined by $f(x)=2^x$ . Which of the following statements is true about the values of $f$ ? Select the two statements that apply.

Use the graph below for questions 3 and 4.

The two lines on the coordinate plane are graphs of functions $f$ and $g$ .

Graph of 2 lines.

Use the graph to explain why the value of $f$ increases by 2 each time the input $x$ increases by 1.

The $y$ -axis counts by 2’s so $f$ must increase 2 each time the input increases 1.
There are two graphs so $f$ increases by 2 each time the input $x$ increases by 1.
$(0, 0)$ and $(1, 2)$ are two points on the graph of $f$ . Between the two points, $y$ increases by 2 and $x$ increases by 1.
$f$ does not increase by 2 each time $x$ increases by 1.

Use the graph to explain why the value of $g$ increases by 2 each time the input $x$ increases by 1. Select two that apply.

$f$ and $g$ never intersect and stay an equal distance apart. $f$ increases by 2 every time $x$ increases by 1, so $g$ must do so as well.
You can’t use the graph because the points are not labeled.
There are two graphs so $g$ increases by 2 each time the input $x$ increases by 1.
$(0, 5)$ and $(1, 7)$ are points on the graph of $g$ . Between the two points, $y$ increases by 2 and $x$ increases by 1.
$(0, 0)$ and $(1, 2)$ are two points on the graph of $g$ . Between the two points, $y$ increases by 2 and $x$ increases by 1.

The function $h$ is given by $h(x)=5^x$ . Find the quotient $\frac{h(x+2)}{h(x)}$ .

The function $h$ is given by $h(x)=5^x$ . Find the quotient $\frac{h(x+3)}{h(x)}$ .

For each of the functions $f, g, h, p$ , and $q$ , the domain is $0≤x≤100$ . For which functions is the average rate of change a good measure of how the function changes for this domain? Select three that apply.

Which of the following statements compare rates of $f(x) = 3x +2$ and $g(x)=3^x$ ?

In $g$ you add 3 to get to the next term; in $f$ you multiply by 3 to get to the next term.
In $f$ you add 3 to get to the next term; in $g$ you multiply by 3 to get to the next term.
In $f$ and $g$ you add 3 to get to the next term.
In $f$ and $g$ you multiply by 3 to get to the next term.

5.15.5 Practice