Question

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. g(x) = (3/2)x

Accepted Answer

Identify the function given: $$g(x) = \left(\frac{3}{2}\right)^x. $$This is an exponential function where the base is $$\frac{3}{2}$$, which is greater than 1, indicating exponential growth. Create a table of values by choosing several values for $$x$$, including negative, zero, and positive integers. For example, select $$x = -2, -1, 0, 1, 2 to $$get a good range of points. Calculate the corresponding $$g(x)$$ values for each chosen $$x by $$substituting into the function: $$g(x) = \left(\frac{3}{2}\right)^x. $$Remember that for negative exponents, $$a^{-n}$$ = \frac{1}{a^n}$$. Plot the points (x$$, g(x))$$ from your table on a coordinate plane. Since the function is exponential growth, the graph should increase as x$ increases and approach zero but never touch the x$-axis as x$ decreases. Use a graphing utility to input g(x$$) = \left(\frac{3}{2}\right)^x$$ and compare the graph with your hand-drawn points to confirm accuracy and understand the shape of the exponential curve.

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. g(x) = (3/2)^x

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Key Concepts

Exponential Functions

Creating a Table of Coordinates

Using Graphing Utilities