Shifting graphs

Summary

• The graph of $f(x)+c$ is the graph of $f(x)$ moved $c$ units upwards (downwards if $c<0$ )
• The graph of $f(x+c)$ is the graph of $f(x)$ moved $c$ units to the left (to the right if $c<0$ )
• The graph of $cf(x)$ is the graph of $f(x)$ stretched vertically (stretched vertically and reflected about the $x$ -axis if $c<0$ )
• The graph of $f(-x)$ is the graph of $f(x)$ reflected about the $y$ -axis.