# Graphing Calculator Drawing: Absolute Value

*Absolute value can be used to draw a person.*

*This post is a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Absolute Value. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-absolute-value/

** Setup.** Navigate to https://www.desmos.com/calculator. Be sure to sign in so that you can save your graph.

** Demonstration - Absolute Value.** Observe the graph as you type each of the following inputs. In general, an absolute value graph $y=m \vert x \vert$ makes a “V” shape, with the magnitude of $m$ controlling the slope of the V, and the sign of $m$ controlling whether the V opens upward or downward.

** Demonstration - Shifts.** Observe the graph as you type each of the following inputs. In general, the graph of $y=m \vert x-a \vert +b$ shifts the absolute value graph $y=m \vert x \vert$ so that the pointy part of the “V” occurs at the point $(a,b).$

** Exercise.** Draw the two absolute value functions shown below. (Hint: Remember that you can limit the domain and range of your functions with parentheses, e.g. $y= \vert x \vert \lbrace -1 < x < 1 \rbrace$ or $y=\vert x \vert \lbrace y < 3 \rbrace.$)

** Exercise.** Draw more absolute value functions to create a person! (The person’s back will be a vertical line, but everything else can be made out of absolute value functions.)

** Challenge.** Try to draw yourself, or your friend! You can include hair, shoes, ears, hands, clothes, etc.)

*This post is a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Absolute Value. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-absolute-value/