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Graphs

Site: Clare-Gladwin RESD
Course: Michigan Algebra I
Book: Graphs
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Date: Wednesday, January 15, 2025, 3:48 PM

Description

Graphs

Table of contents

Writing a Function

An exponential function is written in the form WritingFunctionFromGraph. Recall from the last lesson that the b-value is the common ratio and the a-value is the initial value. On a graph, the a-value will represent the y-intercept since any number raised to the power of zero equals one. If either the y-intercept or the common ratio are known on the graph, you can write a function.


Example 1

Write an exponential function WritingFunctionFromGraph for the graph below.

FuncGraphEx1-1

Step 1. Find the y-intercept

The y-intercept is identified on the graph as (0, 500).

Step 2. Substitute a point into the equation to find the common ratio

FuncGraphEx1-2

Step 3. Substitute the values of a and b into the equation.

y = 500 . FuncGraphEx1-3


Example 2

Write an exponential function for a graph that includes the points (2, 2) and (3, 4).

Step 1. Substitute the values of each point into the function WritingFunctionFromGraph.

1.) 2 = a.b2 2.) 4 = a.b3

Step 2. Solve for "a" using the first function

FuncGraphEx2-1

Step 3. Substitute the value of "a" from step 2 into the second function. And solve for "b".

FuncGraphEx2-2

Step 4. Substitute "b" back into the first function and solve for "a" .

FuncGraphEx2-3

Step 5. Substitute the values of "a" and "b" into the original function WritingFunctionFromGraph.
y = FuncGraphEx2-4 . 2 x

Example 3

Write an exponential function WritingFunctionFromGraph for a graph that includes (2, 4) and (3, 16).

Step 1. Since the two points have an x-increment of 1, the ratio between their y-values is the common ratio. Use this to find the value of b.

FuncGraphEx3-1

Step 2. Substitute either point into WritingFunctionFromGraph, solve for "a."

Using (2,4) FuncGraphEx3-2

Using (3,16) FuncGraphEx3-3

Step 3. Substitute "a" and "b" into the original function WritingFunctionFromGraph.

Video Lesson

To learn how to write an exponential function, watch the following video:

Finding Exponential Models

Guided Practice

To solidify your understanding of writing exponential models, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.

Guided Practice

Practice

Exponential Models Worksheet

Let's Make a Deal Worksheet
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Answer Keys

Exponential Models Answer Key

Let's Make a Deal Answer Key

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Sources

Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project

Holt, Rinehart, & Winston. "Sequences & Functions."

http://my.hrw.com/math06_07/nsmedia/homework_help/msm3/msm3_ch13_05_homeworkhelp.html (accessed September 13, 2010).

Motichka, "Exploring Exponential Models."

http://staffweb.psdschools.org/kemotich/Mrs_Motichka/Algebra%202/Chapter%208/8-1%20Exploring%20exponential%20models.pdf (accessed September 13, 2010).