Question

Explain how you can tell the function f (x) = |x-5| is not linear by using points on its graph?

Answer 1

Absolute value graphs are shaped like a "V" where x = h is the bottom of the "V" when y=|x-h|.

So lets use x=4, 5, and 6. For each x value wee will plug it into the equation to get a y value. If the function were linear, the y values should change at a constant rate in the same direction (slope).

f(4) = 1
f(5) = 0
f(6) = 1

As you can see, the function is not linear because it goes from decreasing to increasing.