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Chapter 3: Problem 14

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$g(x)=\left(\frac{4}{3}\right)^{x}$$

Short Answer

Expert verified
When you create the table of coordinates and plot them on a graph, you will see that \(g(x)=\left(\frac{4}{3}\right)^{x}\) is an exponential function that rises from left to right.

Step by step solution

01

Choosing X-values and Calculating Corresponding Y-values

Choose a range of x-values, for instance, -2, -1, 0, 1, 2. With these selected, substitute each of them into the function \(g(x)=\left(\frac{4}{3}\right)^{x}\) to find the corresponding y-value. This will give you the set of coordinates (x, y)
02

Plotting the Coordinates

Plot each coordinate on a graph. Start at the origin (0,0) and plot the rest of the points relative to it. This will give a visual representation of the function.
03

Drawing the Graph

Connect the points carefully, either by hand or using a graphing tool. The result should be a curve, as the function is exponential.
04

Verification With a Graphing Utility

If a graphing utility is available, input the function \(g(x)=\left(\frac{4}{3}\right)^{x}\) to generate its graph. Compare this with the hand-drawn graph and check for discrepancies. If none are found, the hand-drawn graph is accurate.

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