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Chapter 7: Problem 4

Use a table of coordinates to graph each exponential function. Begin by selecting \(-2,-1,0,1\), and 2 for \(x\). \(y=2^{x-1}\)

Short Answer

Expert verified
The coordinates for the exponential function \(y = 2^{x-1}\) are (-2,0.25), (-1,0.5), (0,1), (1,2), (2,4). Plotting these points and drawing the curve for these points generates the graph of the said function.

Step by step solution

01

Understanding the exponential function

The function \(y=2^{x-1}\) is an exponential function. Here, the base is 2 and it is a transformed function of basic exponential function \(y=2^x\).
02

Create a table of values

Substitute the x-values \(-2,-1,0,1,2\) in the function \(y=2^{x-1}\). Then calculate the corresponding y-values. The results are: \n When x=-2, \(y=2^{-2-1}=0.25\), \n When x=-1, \(y=2^{-1-1}=0.5\), \n When x=0, \(y=2^{0-1}=1\), \n When x=1, \(y=2^{1-1}=2\), \n When x=2, \(y=2^{2-1}=4\).
03

Plot the points and draw the graph

Plot the points (-2,0.25), (-1,0.5), (0,1), (1,2), and (2,4) on the graph. These points should fall on a curve. Connect the plotted points to complete the exponential graph.

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Most popular questions from this chapter

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Use a table of coordinates to graph each exponential function. Begin by selecting \(-2,-1,0,1\), and 2 for \(x\). \(y=2^{x+1}\)
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