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Chapter 7: Problem 3

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 graph of the function \(y = 2^{x+1}\) is an upward-curving line which passes through the points with coordinates -2, -1, 0, 1, and 2 from calculation.

Step by step solution

01

Set up the table of coordinates

Set up a table with columns for \(x\) and \(y\). Write the chosen \(x\)-values of -2,-1,0,1, and 2 in the \(x\)-column of the table.
02

Calculate the corresponding y values

Calculate the corresponding \(y\) values for each \(x\) value using the given function \(y = 2^{x+1}\). Plug each \(x\)-value in the function and calculate the resulting \(y\)-value.
03

Fill in the y-values in the table

After calculating the \(y\)-values, fill them in the \(y\)-column of the table next to their corresponding \(x\)-values.
04

Plot the points on the graph

Plot each point (\(x, y\)) from the table on the graph. Make sure to appropriately scale the axes so all the selected points can be placed on the plot. Each point corresponds to a pair (\(x\), \(y\)) from the table.
05

Connect the points

Finally, connect the plotted points and draw the graph of the function \(y = 2^{x+1}\). The pattern should resemble an upward-curving line, which is typical for an exponential function.

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