$\"\"$

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 1 to each side)

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

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

Next make at table, fill out the table with values for x > 7 and x < 7.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\
f(x) = |x - 7|
\
\
x
\ \
f(x)
\
\
-5
\ \
12
\
\
-3
\ \
10
\
\
0
\ \
7
\
\
3
\ \
4
\
\
5
\ \
2
\
\

First, draw a co-ordinate plane.

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

$\"absolute$

Observe the graphs, both graphs have same shape and points on $\"\"$ are 7 units right than the points on $\"\"$ .

The graph of $\"\"$ is the graph of $\"\"$ and translated 7 units right . $\"\"$

The graph of $\"\"$ is the graph of $\"\"$ and translated 7 units right .

\ *f(x)* = \|x - 7\| \
\ x \	\ *f(x)* \
\ -5 \	\ 12 \
\ -3 \	\ 10 \
\ 0 \	\ 7 \
\ 3 \	\ 4 \
\ 5 \	\ 2 \