$\"\"$

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 3 from each side)

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

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

Next make at table, fill out the table with values for x > -3 and x < -3.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\
f(x) = |x + 5|
\
\
x
\ \
f(x)
\
\
– 10
\ \
5
\
\
-5
\ \
0
\
\
0
\ \
5
\
\
5
\ \
10
\
\
10
\ \
15
\
\

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 3 units left side than the points on $\"\"$ .

The graph of $\"\"$ is the graph of $\"\"$ and translated 3 units left. $\"\"$

The graph of $\"\"$ is the graph of $\"\"$ and translated 3 units left.

\ *f(x)* = \|x + 5\| \
\ x \	\ *f(x)* \
\ – 10 \	\ 5 \
\ -5 \	\ 0 \
\ 0 \	\ 5 \
\ 5 \	\ 10 \
\ 10 \	\ 15 \