Math Exponential functions Stretching and compressing

Stretching and compressing

The graph of an exponential function is stretched or compressed with the factor $a$ parallel to the y-axis. The general formula is:

$y=a\cdot b^x$


  • If $a > 1$, the graph is stretched.
  • If $0 < a < 1$, the graph is compressed.

  • If $a < 0$, the graph is reflected
  • about the x-axis.


$\color{green}{g(x)=2\cdot2^x}$ (stretched)
$\color{brown}{h(x)=\frac12\cdot2^x}$ (compressed)
$\color{grey}{i(x)=-2\cdot2^x}$ (reflected)