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Chapter 3: Problem 22

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=4^{x-3}+3$$

Short Answer

Expert verified
The table of values for the function is: (-1, 1.33), (0, 1.5), (1, 2), (2, 4), (3, 7). The function graph increases as x increases and approaches \( y = 3 \) as \( x \) approaches negative infinity.

Step by step solution

01

Tabulating the Function

Begin by choosing a range of x-values. For the purpose of this exercise, let's choose -1, 0, 1, 2, and 3. Plug these x-values into the function using a graphing utility to get corresponding y-values. The resulting mapping should be: (-1, 1.33), (0, 1.5), (1, 2), (2, 4), (3, 7).
02

Plotting the points

On a Cartesian plane, plot each of these points. The x-coordinate of each point is the x-value, and the y-coordinate is the corresponding y-value.
03

Sketching the Graph

Once all the points are plotted, connect them with a smooth curve to complete the graph of the function. Note the behaviours of the function: it increases as x increases, and it approaches the horizontal line y=3 as x approaches negative infinity.

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