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Chapter 7: Problem 5

Use a table of coordinates to graph each exponential function. Begin by selecting \(-2,-1,0,1\), and 2 for \(x\). \(f(x)=3^{x-1}\)

Short Answer

Expert verified
The y-values for the given x-values (-2,-1,0,1,2) are (1/27, 1/9, 1/3, 1, 3) respectively. Hence the points to plot are \((-2, 1/27)\), \((-1, 1/9)\), \((0, 1/3)\), \((1, 1)\), \((2, 3)\). Plotting these on a graph will give the shape of the function \(f(x)=3^{x-1}\).

Step by step solution

01

Determine the y-values for the function

Firstly, the function \(f(x)=3^{x-1}\) has been given. We have to find the value of \(f(x)\) at \(x=-2,-1,0,1\), and 2. To do this, substitute the x-values into the function:1. When \(x=-2\), \(f(-2)=3^{-2-1}=3^{-3}=1/27\).2. When \(x=-1\), \(f(-1)=3^{-1-1}=3^{-2}=1/9\).3. When \(x=0\), \(f(0)=3^{0-1}=3^{-1}=1/3\).4. When \(x=1\), \(f(1)=3^{1-1}=3^0=1\).5. When \(x=2\), \(f(2)=3^{2-1}=3^1=3\).
02

Create a table of coordinates

After finding the value of \(f(x)\) at \(x=-2,-1,0,1\), and 2, create a table of coordinates. | x | f(x) ||---|--------|-2 | 1/27 ||-1 | 1/9 || 0 | 1/3 || 1 | 1 || 2 | 3 |
03

Graph the function

The next step is to plot these points onto a graph paper and connect these points to form a curve. The points will be :1. \((-2, 1/27)\)2. \((-1, 1/9)\)3. \((0, 1/3)\)4. \((1, 1)\)5. \((2, 3)\)By connecting these points, the exponential function \(f(x) = 3^{x-1}\) can be plotted.

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