$\"\"$

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: $\"\"$ )

$\"\"$ (Multiply each side by negative one)

$\"\"$ (Product of two same signs is positive) $\"\"$

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

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\
f(x) = -|x| + 3
\
\
x
\ \
f(x)
\
\
-2
\ \
1
\
\
-1
\ \
2
\
\
0
\ \
3
\
\
1
\ \
2
\
\
2
\ \
1
\
\

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 higher than the points on $\"\"$ .

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

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

\ *f(x)* = -\|x\| + 3 \
\ x \	\ *f(x)* \
\ -2 \	\ 1 \
\ -1 \	\ 2 \
\ 0 \	\ 3 \
\ 1 \	\ 2 \
\ 2 \	\ 1 \