MathGoldMedalist
Sign InRegister

Toolkit 53

Graphing Functions: Transformations and Absolute Value Functions

Graph of ∣x∣+∣y∣=5|x|+|y|=5:

Graph of |x| + |y| = 5

Graph of (x−3)2+(y−4)2=9(x-3)^2+(y-4)^2=9:

Graph of (x - 3)^2 + (y - 4)^2 = 9

Graph of ∣x−3∣+∣y+2∣=1|x-3|+|y+2|=1:

Graph of |x - 3| + |y + 2| = 1

To graph absolute value equations, split the absolute values into cases, graph each case separately, and then combine the pieces.

Graph of ||x| - 1| + ||y| - 1| = 1

Graph of y=12xy=\dfrac{1}{2x}:

Graph of y = 1/(2x)

Graph Transformations

TransformationExampleDescription
Horizontal Shifty=f(x−3)y=f(x-3)Shift 3 units to the right
Vertical Shifty=f(x)+2y=f(x)+2Shift 2 units upward
Horizontal Stretchy=f(x/2)y=f(x/2)Stretch horizontally by a factor of 2
Horizontal Compressiony=f(2x)y=f(2x)Compress horizontally by a factor of 2
Vertical Stretchy=3f(x)y=3f(x)Stretch vertically by a factor of 3
Vertical Compressiony=12f(x)y=\frac{1}{2}f(x)Compress vertically by a factor of 2
Reflection across the x-axisy=−f(x)y=-f(x)Flip over the x-axis
Reflection across the y-axisy=f(−x)y=f(-x)Flip over the y-axis
Back to Toolkit