$\"\"$

First find the minimum point of the graph.

Since absolute value function can not be negative,

the minimum point of the graph is where $\"\"$ . $\"\"$

The original function is $\"\"$ .

Set original function $\"\"$

$\"\"$

$\"\"$ (Subtract 9 from each side)

$\"\"$ (Apply additive inverse property: $\"\"$ )

$\"\"$ (Apply additive identity property: $\"\"$ ) $\"\"$

Next make at table, fill out the table with values for x > 9 and x < 9.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\
f(x) = | x | + 9
\
\
x
\ \
f(x)
\
\
– 6
\ \
15
\
\
– 3
\ \
12
\
\
0
\ \
9
\
\
3
\ \
12
\
\
6
\ \
15
\
\

\ \

First, draw a co-ordinate plane.

Locate the points on co-ordinate plane and draw the graph through these points.

$\"graph$

Graph for the absolute value function $\"\"$

$\"graph$

Observe the graphs, both graphs have same shape and points

on $\"\"$ are 9 units higher than the points on $\"\"$ .

The graph of $\"\"$ is the graph of $\"\"$ and translated 9 units up. $\"\"$

The graph of $\"\"$ is the graph of $\"\"$ and translated 9 units up.

\ f(x) = \| x \| + 9 \
\ x \	\ f(x) \
\ – 6 \	\ 15 \
\ – 3 \	\ 12 \
\ 0 \	\ 9 \
\ 3 \	\ 12 \
\ 6 \	\ 15 \