Answer
a) $f(x)=x^2$
b) Horizontal shift one unit to the left, reflection across the $x$-axis, vertical shift downward
c) See graph
d) $g(x)=-f(x+1)-3$
Work Step by Step
We are given the function:
$g(x)=-3-(x+1)^2$
a) The parent function is:
$f(x)=x^2$
b) Horizontally shift $f(x)$ one unit to the left to get $a(x)=(x+1)^2$.
Reflect $a(x)$ across the $x$-axis to get $b(x)=-(x+1)^2$.
Vertically shift $b(x)$ 3 units downward to get $g(x)=-3-(x+1)^2$.
c) Graph the transformations:
d) Use function notation to write $g$ in terms of $f$:
$g(x)=-f(x+1)-3$
