Math

Basic Concepts on Linear Functions

Example 2

Given the linear function f defined by $f (x) = 5,$ determine its slope and y-intercept. Then graph the given function.

Solution

The given function $f (x) = 5$ can also be written as $f (x) = 0 x + 5.$ Thus, it is a linear function with slope $m = 0$ and y-intercept $b = 5.$ Its graph is a horizontal line.

In general, a linear function in the form $f (x) = k,$ where k is a constant, is called a constant function. Its graph is a horizontal line with y-intercept k. Its range is the set {k}.