Week 12 – Absolute Value Functions

This week we’ve learned about another Function pattern. Rather than just Standard, Factored and General forms we came across functions involving Absolute values, and what it does it kind of interesting.

An absolute value is a distance or difference between any two numbers on a number line, and the difference cannot be a negative number, because we’re not subtracting it, but we’re measuring it instead.

To graph an Absolute Value Function, first, graph the function ignoring the absolute value symbol and you should get an ordinary slope. Next, indicate the slope under the X-axis as not the real answer, e.g., making it a dotted line. Finally, reflect the said portion of the slope to be over the X-axis so that every solution to the function is a positive value, hence the meaning of absolute values.

Below will be one example of a straight line slope and a parabola, notice how it varies:

The slope’s original Y-intercept was (0,-5), after the negative part of the slope was “reflected”. Now the new Y-intercept is (0,5), forming a V-shape.

This is a parabola under the effects of absolute values. Since the minimum point of this function was on the negative part (under the X-axis), the point bounces back, along with the line, making a reflection over the X-axis again, forming a W-shaped parabola.