### Home > CALC > Chapter 1 > Lesson 1.2.6 > Problem1-94

1-94.

Given $f(x) = (x - 3)^2 + 4$ and $g ( x ) = \frac { 1 } { x - 4 } - 2$, find and simplify the following:

1. $h(x)= f(x + 2) - 5$

$h(x) = f(x + 2) = 5$
$h(x) = [((x + 2) − 3)^ 2] + 4 − 5$
Simplify.

2. $k(x) = g(3 - x) + 2$

$(3 - x)$, the horizontal shift, will replace '$x$' in the $g(x)$ function.
$+2$, the vertical shift, will be added to the entire '$g(x)$' function.

3. Using set notation, find the domain and range for $g(x)$ and $k(x)$.

Consider the parent graphs of $f$ and $g$.
Domain and range will shift from that of the parent.
The parent graph of $f(x)$ is $y = x^2$.
What is the parent graph of $g(x)$?