Answer
(a) See the image below.
(b) As we can visually see in the image applying larger values of $a$ causes the graph to shrink vertically and stretch horizontally.
Work Step by Step
(a) Using the base function: $f(x)=\frac{a}{2}(e^{\frac{x}{a}}+e^{-\frac{x}{a}})$ We can input the following numbers of $a=0.5, 1, 1.5, 2$ and then using a graphing calculator graph them.
$a=0.5$
$f(x)=\frac{0.5}{2}(e^{\frac{x}{0.5}}+e^{-\frac{x}{0.5}})$ (Black graph)
$a=1$
$f(x)=\frac{1}{2}(e^{\frac{x}{1}}+e^{-\frac{x}{1}}) = \frac{1}{2}(e^x+e^{-x})$ (Blue graph)
$a=1.5$
$f(x)=\frac{1.5}{2}(e^{\frac{x}{1.5}}+e^{-\frac{x}{1.5}})$ (Green graph)
$a=2$
$f(x)=\frac{2}{2}(e^{\frac{x}{2}}+e^{-\frac{x}{2}})=e^{\frac{x}{2}}+e^{-\frac{x}{2}}$ (Red graph)
(b) As we can visually see in the image applying larger values of $a$ causes the graph to shrink vertically and stretch horizontally.
