$\"\"$

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 2.5 to each side)

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

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

Next make at table, fill out the table with values for $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\
f(x) = |x| - 2.5
\
\
x
\ \
f(x)
\
\
-2
\ \
-0.5
\
\
-1
\ \
-1.5
\
\
0
\ \
-2.5
\
\
1
\ \
-1.5
\
\
2
\ \
-0.5
\
\

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 2.5 units lower than the points on $\"\"$ .

The graph of $\"\"$ is the graph of $\"\"$ and translated 2.5 units down.

$\"\"$

The graph of $\"\"$ is the graph of $\"\"$ and translated 2.5 units down.

\ *f(x)* = \|x\| - 2.5 \
\ x \	\ *f(x)* \
\ -2 \	\ -0.5 \
\ -1 \	\ -1.5 \
\ 0 \	\ -2.5 \
\ 1 \	\ -1.5 \
\ 2 \	\ -0.5 \