Free Printable 5.2C Writing and Graphing Exponential Functions

1.

What is the domain of f(x)?

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\frac{1}{200},\ \infty\right)$

c)

$\left(-\infty,\ 0\right)$

d)

$\left[-\frac{1}{200},\ -50\right]$

2.

What is the range of f(x)?

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\frac{1}{200},\ \infty\right)$

c)

$\left(-\infty,\ 0\right)$

d)

$\left(0,\ \infty\right)$

3.

What is the y-intercept of f(x)?

a)

$-2$

b)

$-\frac{1}{200}$

c)

$-\frac{1}{2}$

d)

$0$

4.

What is the asymptote of f(x)?

a)

$y=-2$

b)

$y=-\frac{1}{200}$

c)

$y=-\frac{1}{2}$

d)

$y=0$

5.

Is f(x) strictly increasing or decreasing? And on what interval?

a)

Increasing on $\left(-\infty,\ \infty\right)$

b)

Increasing on $\left(-\infty,\ 0\right)$

c)

Decreasing on $\left(-\infty,\ \infty\right)$

d)

Decreasing on $\left(0,\ \infty\right)$

6.

Is f(x) strictly positive or negative? And on what interval?

a)

Positive on $\left(-\infty,\ \infty\right)$

b)

Positive on $\left(-\infty,\ 0\right)$

c)

Negative on $\left(-\infty,\ \infty\right)$

d)

Negative on $\left(0,\ \infty\right)$

7.

Write the function f(x).

a)

$f\left(x\right)=-2\left(-\frac{1}{200}\right)^x$

b)

$f\left(x\right)=-\frac{1}{200}\left(5\right)^x$

c)

$f\left(x\right)=-\frac{1}{2}\left(10\right)^x$

d)

$f\left(x\right)=-\frac{1}{2}\left(5\right)^x$

8.

Select BOTH statements that identify the end behavior of f(x).

a)

$As\ x\rightarrow-\infty,\ y\rightarrow-\infty$

b)

$As\ x\rightarrow-\infty,\ y\rightarrow\infty$

c)

$As\ x\rightarrow\infty,\ y\rightarrow-\infty$

d)

$As\ x\rightarrow\infty,\ y\rightarrow0$

e)

$As\ x\rightarrow-\infty,\ y\rightarrow0$

9.

Write the function for the following table:

a)

f(x) = 1(3)^x

b)

f(x) = 3(3)^x

c)

f(x) = 3x+3

d)

f(x)= 6x+1

10.

What does the y-intercept of the graph represent?

a)

The amount of grams the material is gaining.

b)

The amount of grams the material is losing.

c)

The amount of grams remaining after so many years.

d)

The initial amount of grams.

11.

What is the average rate of change between when x = -1 and x = 0?

a)

-2

b)

2

c)

1/2

d)

-1/2

12.

What is the average rate of change over the interval [0,3]?

a)

21

b)

-21

c)

1/21

d)

-1/21

13.

If $g\left(x\right)=3\left(2\right)^x$ , what is the average rate of change over the interval $1\le x\le5$ ?

a)

22.5

b)

90

c)

30.25

d)

25

14.

Iris founded a new town, Iristown. The population of Iristown after x years can be modeled by the function p(x) = 1500(1.1)^x. On average, how fast is the population increasing between years 0 and 10?

a)

~212 people/year

b)

~251 people/year

c)

~239 people/year

d)

~391 people/year

15.

The number of decks of popular trading cards is a function f of the number of days d since the shipment arrived.

Interpret the average rate of change for the first 5 days.

a)

The store lost an average of 143.3 popular trading cards each day for the first 5 days.

b)

The store gained an average of 143.3 popular trading cards each day for the first 5 days.

c)

The store lost an average of 143.3 popular trading cards each year for the first 5 years.

d)

The store lost an average of 0.007 popular trading cards each day for the first 5 days.

16.

What is the DOMAIN of the function and how does it relate to the real-world context? (Click on the picture to make it larger!)

a)

$x\ge0$ The amount of years cannot be negative.

b)

$x\ge0$ The amounts of years is strictly decreasing.

c)

$IR$ The amount of years has no restrictions.

d)

$x>0$ The amount of years can only be positive.

17.

What is the RANGE of the function and how does it relate to the real-world context? (Click on the picture to make it larger!)

a)

$y\le500$ The value of the computer is always $500 or less.

b)

$y>0$ The value of the computer is always positive.

c)

$0<y\le500$ The value of the computer is always more than $0 and no more than $500.

d)

$y<500$ The value of the computer is always less than $500.

18.

What is the ASYMPTOTE of the function and how does it relate to the real-world context? (Click on the picture to make it larger!)

a)

$y=500$ The value of the computer approaches $500, but never reaches $500.

b)

$y=0$ The value of the computer approaches $0, but never reaches $0.

c)

$x=0$ The value of the computer approaches $0, but never reaches $0.

d)

$y=0$ The value of the computer will someday be negative.

e)

$x=0$ The years approach 0 but never reach 0.

19.

What is the END BEHAVIOR of the function and how does it relate to the real-world context? (Click on the picture to make it larger!)

a)

As $x\rightarrow\infty$ , $y\rightarrow-\infty$ As the years continue, the value of the computer continues to decrease.

b)

As $x\rightarrow\infty$ , $y\rightarrow0$ As the years continue, the value of the computer becomes more and more negative.

c)

As $x\rightarrow-\infty$ , $y\rightarrow0$ Going back in history, the value of the computer gets closer to being $0

d)

As $x\rightarrow-\infty$ , $y\rightarrow\infty$ As the years continue, the value of the computer also increases.

e)

As $x\rightarrow\infty$ , $y\rightarrow0$ As the years continue, the value of the computer gets closer to being $0.

20.

An emergency comes up and you need to borrow $20 from your friend. Your friend says yes, but charges you interest. They give you two options for the loan. You can either:

A. Pay back the initial $20 plus $1 per day

B. Pay back starting with an initial fee of $0.50 and it triples each day.

Which is the better option after just 4 days?

a)

Option A

b)

Option B

5.2C Writing and Graphing Exponential Functions

Total questions: 20

Worksheet time: 15mins

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