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Chapter 7: Problem 6

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
For the exponential function \(f(x) = 3^{x+1}\), the coordinates of the graph are \((-2, 0.33), (-1,1), (0,3), (1,9), and (2,27)\)

Step by step solution

01

Understand the Function

The function given is \(f(x) = 3^{x+1}\), which is an exponential function. This function will be used to generate the y-coordinates for the given x-values (-2,-1,0,1,2).
02

Compute the y-Coordinates

Substitute each x-coordinate into the function to find the corresponding y-coordinate:For \(x=-2\), \(f(-2)=3^{-1}=0.33\)For \(x=-1\), \(f(-1)=3^{0}=1\)For \(x=0\), \(f(0)=3^{1}=3\)For \(x=1\), \(f(1)=3^{2}=9\)For \(x=2\), \(f(2)=3^{3}=27\)
03

Fill out the Table of Coordinates

Having calculated the y-values for a given x, coordinates for the graph are as follows: \((-2, 0.33), (-1, 1), (0, 3), (1, 9), (2, 27)\)
04

Graph the Function

Plot each pair of coordinates from the table on a graph. Connect the points to represent the exponential function \(f(x)=3^{x+1}\).

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Most popular questions from this chapter

Each group member should consult an almanac, newspaper, magazine, or the Internet to find data that can be modeled by linear, exponential, logarithmic, or quadratic functions. Group members should select the two sets of data that are most interesting and relevant. Then consult a person who is familiar with graphing calculators to show you how to obtain a function that best fits each set of data. Once you have these functions, each group member should make one prediction based on one of the models, and then discuss a consequence of this prediction. What factors might change the accuracy of the prediction?

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