Answer
a) $f(x)=x^2$
b) Vertical shrink, vertical shift
c) See graph
d) $g(x)=\dfrac{1}{2}f(x)-2$
Work Step by Step
We are given the function:
$g(x)=\dfrac{1}{2}x^2-2$
a) The parent function is:
$f(x)=x^2$
b) Vertically shrink $f(x)$ by a factor of $\dfrac{1}{2}$ to get $a(x)=\dfrac{1}{2}x^2$.
Vertically shift $a(x)$ 2 units downward to get $g(x)=\dfrac{1}{2}x^2-2$.
c) Graph the transformations.
d) Use function notation to write $g$ in terms of $f$:
$g(x)=\dfrac{1}{2}f(x)-2$
