$\"\"$

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 $\"\"$

$\"\"$

$\"\"$ (Add 8 to each side)

$\"\"$ (Additive inverse property: $\"\"$ )

$\"\"$

Next make at table, fill out the table with values for x > 8 and x < 8.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\
f(x) = |x| - 8
\
\
x
\ \
f(x)
\
\
– 2
\ \
– 6
\
\
–1
\ \
– 7
\
\
0
\ \
– 8
\
\
1
\ \
– 7
\
\
2
\ \
– 6
\
\

First, draw a co-ordinate plane.

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

$\"absolute$

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

$\"absolute$

Observe the graphs, both graphs have same shape and points on $\"\"$ are 8 units lower than the points on $\"\"$ . \ \

The graph of $\"\"$ is the graph of $\"\"$ and translated 8 units down. \ \

$\"\"$

The graph of $\"\"$ is the graph of $\"\"$ and translated 8 units down.

\ *f(x)* = \|x\| - 8 \
\ x \	\ *f(x)* \
\ – 2 \	\ – 6 \
\ –1 \	\ – 7 \
\ 0 \	\ – 8 \
\ 1 \	\ – 7 \
\ 2 \	\ – 6 \