Page 745 - Algebra 1

A graphing calculator is helpful with comparing graphs of functions and formulating rules based on the values of a and b.
Comparing Graphs
Using a graphing calculator, graph each pair of functions on the same screen. Tell how the graphs are alike and how they are different.
a. y = 3(2)x and y = -3(2)x
SOLUTION
Use to enter the equations. Use to graph the equations.
Alike: Both graphs are symmetric about the x-axis. For any x-value, the absolute values of the corresponding y-values are the same.
Different: When a = 3, the y-values increase from left to right. When a = -3, the y-values decrease from left to right.
x _1x b. y=3(2) andy=3(2)
SOLUTION
Alike: Both graphs are above the x-axis and symmetric about the y-axis. For any y-value, the absolute values of the corresponding x-values are the same.
Different: When b = 2, the y-values increase from left to right. When b = _1 , the y-values decrease from left to right.
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Application: Population
The exponential function y = 12.28(1.00216)x models the approximate population of Pennsylvania from 2000 to 2006, where x is the number of years after 2000 and y represents millions of people. Use a graphing calculator to find the approximate population of Pennsylvania in 2005. Assuming the model does not change, when will the population reach 13 million?
Example
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Hint
Use 6 to set the intervals on the x-axis and y-axis from -10 to 10.
Math Reasoning
Generalize For which values of b, 2 or _1 , do
2
the y-values approach
0 as x increases? As x decreases?
Example
5
730 Saxon Algebra 1