Question

1. on the set of axes below, graph $f(x) = |x - 3| + 2$.

state the domain:
$(-8, 8)$
all real numbers

Explanation:

Step1: Choose x-values for table

Select x-values around the vertex's x-coordinate (3, since the vertex of $|x-h|+k$ is at $(h,k)$). Let's pick $x=1,2,3,4,5$.

Step2: Calculate f(x) for each x

For $x=1$: $f(1)=|1-3|+2=|-2|+2=2+2=4$
For $x=2$: $f(2)=|2-3|+2=|-1|+2=1+2=3$
For $x=3$: $f(3)=|3-3|+2=0+2=2$
For $x=4$: $f(4)=|4-3|+2=|1|+2=1+2=3$
For $x=5$: $f(5)=|5-3|+2=|2|+2=2+2=4$

Step3: Confirm domain of absolute value function

Absolute value functions have no restrictions on input x-values.

Answer:

Completed Table:

$x$	$f(x)$
2	3
3	2
4	3
5	4

Domain:

All real numbers (or $(-\infty, \infty)$)