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Chapter 3: Problem 13

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$g(x)=\left(\frac{3}{2}\right)^{x}$$

Short Answer

Expert verified
The graph starts at the point (0,1), it increases and passes through the points (-2, 0.25), (-1, 0.67), (1, 1.5), and (2, 2.25). As x increases, the graph climbs steeply. As x decreases, the graph approaches but never reaches the x-axis.

Step by step solution

01

Select points to graph

Choose a few points for x. Good points to start with are -2, -1, 0, 1, and 2. These numbers give a good sketch of the function's behavior.
02

Calculate function's values

Calculate \(g(x)\) for every \(x\) chosen. You should get the following pairs (x, g(x)): (-2, 0.25), (-1, 0.67), (0,1), (1, 1.5), and (2, 2.25)
03

Plot the coordinates

Plot each of these points on your graph.
04

Draw the curve

Now, connect all the points with a smooth curve. Also, it is important to illustrate the trend that the curve takes as it stretches out towards the edges of the graph, here it should continue upwards to the right and flatten out towards the x-axis to the left.
05

Confirm with a graphing utility

Lastly, confirm your hand-drawn graph with a reliable graphing utility. They should match closely.

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