Graph Transformations

f(x)=(x-k)

Horizontal shift. If k is negative shift the graph to the right. If k is positive shift the graph to the left.

y= f(Ax)

Horizontal stretch or shrink. Multiply each x value by one over A

y= -f(-x)

Reflection over the x and y axis. This means you change both the x and y values.

y= -f(x)

Reflection over the x axis. This means you change the signs to all of the y values. This will result in the graph moving to one side of the x axis.

y= f(-x)

Reflection over the y axis. This means you change the sign to all x values. This cause the graph to move to one side of the y axis.

f(x)=x + k

Vertical shift. If k is positive move the graph up. If k is negative move the graph down.

y= A f(x)

Vertical stretch or shrink. Multiply y values by A. If A is greater than 1 the graph will stretch, if A is less than 1 the graph will shrink