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.