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Chapter 1: Problem 15

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=2.5 x-4.25$$

Short Answer

Expert verified
The line for the function \(f(x) = 2.5x - 4.25\) rises by 2.5 units for every single unit move to the right, and it intersects the y-axis at -4.25.

Step by step solution

01

Identify the type of function

The given function \(f(x) = 2.5x - 4.25\) is a linear function. It is in the form \(y = mx + b\), where \(m = 2.5\) is the slope and \(b = -4.25\) is the y-intercept.
02

Use Graphing Utility

Enter the function \(f(x) = 2.5x - 4.25\) into the graphing utility. Start by having the viewing window set to standard settings (For example, \(x\) values from -10 to 10 and \(y\) values from -10 to 10).
03

Adjust Viewing Window

If the line is not fully visible, adjust the viewing window accordingly until the full view of the line is seen. The crucial points are usually the \(x\)- and \(y\)-intercepts.
04

Analyze the graph

Using the graph, confirm that the slope is \(2.5\) and the y-intercept is \(-4.25\). The line should rise by \(2.5\) units for every single unit move to the right, and it should intersect the y-axis at \(-4.25\).

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