Graph Exponential Functions Exponential Function a function defined by an equation of the form y = abx, where 7-5 Study Guide and Intervention ( continued)
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Study Guide and Intervention (continued) not contain variables with exponents other than 1 a transformation in which a figure is enlarged or reduced
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.
NAME DATE PERIOD
Lesson 7-5
Chapter 7 29 Glencoe Algebra 1
7-5Graph Exponential Functions
Exponential Functiona function de? ned by an equation of the form y = ab x , where a ≠ 0, b > 0, and b ≠ 1You can use values of
x to find ordered pairs that satisfy an e x ponential function. Then you can use the ordered pairs to graph the function.Graph y = 3
x . Find the y -intercept and state the domain and range.xy 2 1 9 1 1 3 01 13 29The y-intercept is 1.
The domain is all real numbers, and the
range is all positive numbers.xy OGraph y = (
1 4 x . Find the y- intercept and state the domain and range.The y-intercept is 1.
The domain is all real numbers, and the range
is all positive numbers.xy O28Exercises
Graph each function. Find the
y -intercept and state the domain and range.1. y = 0.3
x2. y = 3x + 1 3. y =
1 3 x + 1 xy O 12 xy O2 16 4 812xy O 12
1; D = {all real 2; D = {all real 2; D = {all real
numbers}, numbers}, numbers}, R = {y|y > 0} R = {y|y > 1} R = {y|y > 1}Example 1Example 2
xy 2 16 1 4 01 1 1 4 2 1 16Study Guide and Intervention
Exponential Functions
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.NAME DATE PERIOD
Chapter 7 30 Glencoe Algebra 1
7-5Study Guide and Intervention (continued)
Exponential Functions
Identify Exponential Behavior It is sometimes useful to know if a set of data is exponential. One way to tell is to observe the shape of the graph. Another way is to observe the pattern in the set of data. Determine whether the set of data shown below displays exponential behavior. Write yes or no. Explain why or why not.Method 1:
Look for a Pattern
The domain values increase by regular
intervals of 2, while the range values have a common factor of 1 2 . Since the domain values increase by regular intervals and the range values have a common factor, the data are probably exponential.Method 2: Graph the DataThe graph shows rapidly decreasing values of y as x increases. This is characteristic of exponential behavior.
Exercises
Determine whether the set of data shown below displays exponential behav ior.Write yes or no. Explain why or why not.
1. x0123 y5101520 2. x0123 y3 9 27 81 No; the domain values are at regular Yes; the domain values are at intervals, and the range values have regular intervals, and the range a common difference 5. values have a common factor 3. 3. x-1135 y32 16 8 4 4. x-10123 y33333 Yes; the domain values are at No; the domain values are at regular intervals, and the range regular intervals, but the range values have a common factor 1 2 . values do not change. 5. x-50510 y1 0.5 0.25 0.125 6. x01234 y 1 3 1 9 1 271 81
1 243
Yes; the domain values are at Yes; the domain values are at regular intervals, and the range regular intervals, and the range values have a common factor 0.5. v alues have a common factor 1 3