Pre-AP Algebra 2

Unit 9 Lesson 4 – Introduction to exponential functions

Objectives: Students will be able to graph functions in the form y = a * bx, where b > 1. Students will determine that the

coefficient represents the y-intercept, as well as affecting the shape of the graph.

Materials: Do Now worksheets and answers overhead; lottery problem overhead; pair work handout and overheads,

overhead calculator

Time Activity

10 min Review Homework

15 min

Quiz 9-1

20 min Group Work Put the Lottery Problem on the overhead and read through it as a class. Give the groups 10 minutes to

discuss the problem and come up with an answer.

Tally the choices on the board. Call on teams to defend their choices.

How can we model the two lottery options?

A(x) = 2,000,000

B(x) = 150,000x

C(x) = 2x (point out that 2

0 = 1, so on the first day, you start with $1)

Note that the last function is one that we haven’t seen before. Why? Because the variable is in the

exponent. This is called an exponential function and you will learn how to graph those in the following

pair work.

25 min Pair Work

Hand out the graphing worksheet.

20 min Direct Instruction

1) Discuss the fact that exponential functions grow very quickly. On the overhead calculator,

graph options A, B, and C, and show that 2x eventually gets much larger. (The range for y

should go from 0 to 25,000,000 and the domain for x should go from 0 to 31) Propose some

alternatives to the problem – would your answer change if the amount of time changed? If it is

less than 13 days, you’d want option A, from 13 to 21 days option B is best, and above 21 days

option C is best.

2) Put the second page on the overhead and work through it together.

Homework #9-4: Exponential Functions 1

Pre-AP Algebra 2 Name: __________________________

Quiz #9-1 Score: /32

Quiz 9-1

Evaluate the logarithm without using a calculator (1 points each)

1) 8log 2 2) 1log 6

3) 5log5 4) 27log 3/1

Expand the expression (2 points each)

5) x4log3 6) z

yx 52

7

4log

Condense the expression (2 points each)

7) 6log24log 55 8) x888 log2

13log26log

Find the exact solution. (4 points each)

9) 25923 x

10) )13(log)85(log 66 xx

12) log

332x 10

13) 3)7(log3 x

14) 2)7(log)2(log 44 xx

Bonus (5 points)

Prove: ACA b

C

b loglog

You won the lottery (cause you are so

awesome)! You are given the choice between

three different options. Which would you

take?

A) A lump sum of 2 million dollars.

B) $100,000 a day for a month.

C) You start with $1 in a new bank account.

Each day for a month, the bank doubles

the amount that you have.

Explain your reasoning.

Pre-AP Algebra 2 Name: ________________________

9-4 Pair Work

Graphing Exponential Functions

1) Make a table for the function ( ) 2xf x in the domain [-4, 4], using only integer values of x.

2) Graph f(x) on the axes.

3) Explain why the graph “flattens out” as x -. Describe the end behavior of f(x) using the

appropriate notation.

4) Using the same domain, make a table for each of the following functions, and graph them on the

same set of axes. Make sure to label each graph with its function name.

1( ) 2

4

xg x ( ) 2xh x 1

( ) 22

xs x

5) Describe the effect that the leading coefficient has on the graph.

Summary: f(x) = abx, b > 1

This is called an __________________________________.

How do you find the y-intercept of this function?

Why is there a horizontal asymptote in only one direction?

How do you find the x-intercepts of this function?

How do you make an easy sketch of this function?

1) Pick the three easy x-coordinates to work with: 1, 0, and -1. Plug them in to find their

matching y-coordinates and plot them. In general, these will be the points:

( , ) ( , ) ( , )

2) Look at the leading coefficient a to determine the end behavior to the right. In other words,

will f(x) +∞ or -∞?

3) Remember that there is a horizontal asymptote to the left at y = 0.

4) Plot any more needed points, and make a smooth curve. Put the arrows on the ends.

Try some on the next page…

Sketch the following:

1( ) 3

2

xf x

3( )

2

x

f x

Pre-AP Algebra 2 Name: ________________________

Homework #9-4

Homework #9-4: Exponential Functions 1

1) Solve for x. Remember to rewrite all terms with the same base first.

a. 2 33 3 3x b. 2 33 3 9x c. 1 2

1 622

2x

d. 1 532 32 8x e. 13 81x f. 1 2 15

5

x

Challenge (+2 if you get this right!): 2 2 1

82

x x

2) Plot points at the x-values -1, 0, and 1 and then sketch the entire exponential function.

( ) 2 3xf x

1 5( )

2 2

x

f x

Match the graphs I.

Match the graphs of f(x), g(x), h(x), and i(x) to the correct exponential functions.

_____ 1(2)x _____ 3(5)x _____ 1(

1

2)x

_____ 3(2)x

Match your own graph I

Make a table of values for the function d(x) 5(

1

2)x

.

Now sketch a graph to go with the function d(x) 5(

1

2)x

on the axes below.

Match the graphs II.

Match the graphs of f(x), g(x), h(x), and i(x) to the correct exponential functions.

_____ 2(3)x _____ 3(5)x _____ 3(5)x _____ 1(

1

3)x

Match your own graph II

Make a table of values for the function d(x) 1(2)x .

Now sketch a graph to go with the function d(x) 1(2)x on the axes below.

The Lottery Problem revisited

The Texas Lottery has decided to give cash allowances as awards to students at DHS. Very nice!

Each of the awards has a different duration and students can pick any of the 3 payment plans (where

the total amount of money received by day x can be modeled by f(x), g(x), and h(x)).

Graph the functions on your calculator and then sketch what they look like in the box. Be sure

that you use an appropriate zoom that shows all three functions.

Payment Plans

f (x) 300 (

4

3)x

g(x) (

4

3)x

h(x) (

4

3)x2

For each of the awards below, decide which payment plan would give each student the most

money to spend on their college education and what the total money given will be. You can use

your graph or algebra to answer.

School Spirit Award

Given to students who have perfect attendance.

Duration: 28 days

Ideal Payment Plan:

Total value of Award:

Perseverance Award

Given to who give 110% of themselves to every endeavor every day.

Duration: 14 days

Ideal Payment Plan:

Total value of Award:

High Academic achievement Award

Given to those who understand why the Perseverance Award, if taken literally, can never be earned.

Duration: 21 days

Ideal payment plan:

Total value of Award:

STAAR Practice

1) A monthly cell phone plan charges $5.00 for the first 300 text messages used and $0.15 for each

additional message. On this plan, what is the number of test messages that must be used in a

month in order to make the average cost per message $0.05?

a. 400

b. 350

c. 900

d. 500

2) Which function is the inverse of ( ) a. ( ) ( ) b. ( ) ( )

c. ( ) ( ) d. ( ) ( )

3) The graph of the function is shown below.

Which grid shows the graph of ?

4) What value of is a solution to the equation √ Record your answer and fill in the

bubbles on your answer document.