# Changes over Equal Intervals

19 questions

# Changes over Equal Intervals

##### Problem 1

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

$f$($x$)=3$x$+5

$f$($x$)=5$x$+3

$f$($x$)=$5^{x}$

$f$($x$)=$x^{5}$

##### Problem 2

2) The function $f$ is defined by $f(x) = 2^x$. Which of the following statements is true about the values of $f$? Select $\textbf{all}$ that apply. Write each corresponding letter in the answer box and separate letters with commas.

a) When the input $x$ increases by 1, the value of $f$ increases by 2.

b) When the input $x$ increases by 1, the value of $f$ increases by a factor of 2.

c) When the input $x$ increases by 3, the value of $f$ increases by 8.

d) When the input $x$ increases by 3, the value of $f$ increases by a factor of 8.

e) When the input $x$ increases by 4, the value of $f$ increases by a factor of 4.

##### Problem 3

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

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

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

##### Problem 4

The function $h$ is given by $h(x) = 5^x$

5) Find the quotient $\frac{h(x + 2)}{h(x)}$.

6) What does this tell you about how the value of $h$ changes when the input is increased by 2?

7) Find the quotient $\frac{h(x + 3)}{h(x)}$.

8) What does this tell you about how the value of $h$ changes when the input is increased by 3?

##### Problem 5

9) For each of the functions $f, g, h, p,$ and $q$, the domain is $0 \leq x \leq 100$. For which functions is the average rate of change a good measure of how the function changes for this domain? Select $\textbf{all}$ that apply. Write each corresponding letter in the answer box and separate letters with commas.

a) $f(x) = x + 2 \quad\quad$ b) $g(x) = 2^x \quad\quad$ c) $h(x) = 111x - 23 \quad\quad$ d) $p(x) = 50,000 \cdot 3^x \quad\quad$ e) $q(x) = 87.5 \quad\quad$

##### Problem 6

10) The average price of a gallon of regular gasoline in 2016 was $2.14. In 2017, the average price was $2.42 a gallon—an increase of 13%.

At that rate, what will the average price of gasoline be in 2020?

##### Problem 7

11) A credit card charges a 14% annual nominal interest rate and has a balance of $500.

If no payments are made and interest is compounded quarterly, which expression could be used to calculate the account balance, in dollars, in 3 years?

500$\cdot$(1+0.14$)^{3}$

500$\cdot\left(1+\frac{0.14}{4}\right)^{3}$

500$\cdot\left(1+\frac{0.14}{4}\right)^{12}$

500$\cdot\left(1+\frac{0.14}{4}\right)^{48}$

##### Problem 8

Here are equations that define four linear functions. For each function, write a verbal description of what is done to the input to get the output, and then write the inverse function.

$a(x) = x - 4$

12) Write a verbal description of what is done to the input to get the output for $a(x)$.

13) Write the inverse function.

$b(x) = 2x - 4$

14) Write a verbal description of what is done to the input to get the output for $b(x)$.

15) Write the inverse function.

$c(x) = 2(x - 4)$

16) Write a verbal description of what is done to the input to get the output for $c(x)$.

17) Write the inverse function.

$d(x) = \frac{x}{4}$

18) Write a verbal description of what is done to the input to get the output for $d(x)$.

19) Write the inverse function.