Reflecting Graphs

To reflect a graph of $LaTeX: y=f\left(x\right)\:$ $y=f\left(x\right)\:$ across the x-axis, make the graph of $LaTeX: -f\left(x\right).$ $-f\left(x\right).$

If instead you want to reflect the graph of $LaTeX: y=f\left(x\right)\:$ $y=f\left(x\right)\:$ across the y-axis, make a graph of $LaTeX: f\left(-x\right).$ $f\left(-x\right).$

You can even flip the graph across both the x-axis and the y-axis by graphing $LaTeX: -f\left(-x\right).$ $-f\left(-x\right).$

If you go to Desmos.com/calculator Links to an external site. , you can play with the free graphing calculator there online to see how this works with some of the common functions introduced earlier in this chapter. Here is another Khan video that does exactly that: