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Chapter 1: Problem 16

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=\frac{5}{6}-\frac{2}{3} x$$

Short Answer

Expert verified
The graph of the function \(f(x)=\frac{5}{6}-\frac{2}{3} x\) is a straight line that intercepts the y-axis at \(\frac{5}{6}\) and descends to the right, showing a negative slope of \(-\frac{2}{3}\). The appropriate viewing window to graph this function can be from -10 to 10 for both x and y.

Step by step solution

01

Identify the function

The function given is a linear function in the form of \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. In this case, \(m = -\frac{2}{3}\) (negative means it's a descending line) and \(b = \frac{5}{6}\), which is where the line intercepts the y-axis.
02

Choose the appropriate viewing window

Since it's a linear function, the plot will be a straight line extending in both the positive and negative direction. Therefore, a good choice of the viewing window would have a range for both x and y that includes zero and extends to a range that can clearly show the slope and y-intercept of the function, such as -10 to 10 for both x and y.
03

Graph the function on the graphing utility

Enter the function \(\frac{5}{6}-\frac{2}{3} x\) into the graphing utility. The line should intercept the y-axis at \(\frac{5}{6}\) and descend to the right, indicating a negative slope of \(-\frac{2}{3}\).

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