Question

a1.4.16
name: __________ date ___ period __
problems 1-3: write each expression as a single integer.

1. $|-4|$
2. $|7| - 2$
3. $|-6| + 1$
4. graph $g(x) = |x + 1| + 4$. use the table if it helps with your thinking.
5. match each function with its graph.

$f(x) = |x + 3| + 2$ ____________
$g(x) = |x - 3| - 2$ ____________
$h(x) = |x - 3| + 2$ ____________

Explanation:

Step1: Evaluate absolute value

$|-4| = 4$

Step2: Evaluate absolute value then subtract

$|7| - 2 = 7 - 2 = 5$

Step3: Evaluate absolute value then add

$|-6| + 1 = 6 + 1 = 7$

Step4: Calculate table values for $g(x)$

For $x=-3$: $g(-3)=|-3+1|+4=|-2|+4=2+4=6$
For $x=-1$: $g(-1)=|-1+1|+4=|0|+4=0+4=4$
For $x=0$: $g(0)=|0+1|+4=|1|+4=1+4=5$
(Add optional $x=1$: $g(1)=|1+1|+4=2+4=6$; $x=2$: $g(2)=|2+1|+4=3+4=7$)

Step5: Identify vertex shifts for matching

1. $f(x)=|x+3|+2$: Vertex at $(-3,2)$ (left 3, up 2) → matches leftmost V-graph
2. $g(x)=|x-3|-2$: Vertex at $(3,-2)$ (right 3, down 2) → matches lowest right V-graph
3. $h(x)=|x-3|+2$: Vertex at $(3,2)$ (right 3, up 2) → matches upper right V-graph

Answer:

1. $4$
2. $5$
3. $7$
4. Completed table:

$x$	$g(x)$
$-1$	$4$
$0$	$5$
$1$	$6$
$2$	$7$

Graph: Plot the points and draw a V-shape with vertex at $(-1,4)$, opening upwards.
5.

• $f(x)=|x+3|+2$: Leftmost V-graph
• $g(x)=|x-3|-2$: Lowest right V-graph
• $h(x)=|x-3|+2$: Upper right V-graph