Explanation:
With the equation
y
=
|
−
x
+
3
|
−
4
, we know that the term inside the absolute value mark will never be less than zero, which means the smallest
y
can be is
y
=
−
4
. This value is achieved with
|
−
x
+
3
|
=
0
, putting
x
=
3
. So that is our first point,
(
3
,
−
4
)
.
We're dealing with
x
terms (versus
x
2
or
√
x
or any other form of
x
), so the graph coming off
(
3
,
−
4
)
will be lines. Since there the coefficient of the
x
term is 1, the slope of those lines will be 1 and
−
1
(with the x term inside the absolute value, we look at both
±
1
).
The standard graph for an absolute value graph is for it to be in the shape of a V. And so we can expect our graph to have points
(
4
,
−
3
)
and
(
2
,
−
3
)
- and we can plug in those values to prove it:
y
=
|
−
x
+
3
|
−
4
−
3
=
|
−
4
+
3
|
−
4
−
3
=
|
−
1
|
−
4
−
3
=
1
−
4
−
3
=
−
3
and
−
3
=
|
−
2
+
3
|
−
4
−
3
=
|
1
|
−
4
−
3
=
1
−
4
−
3
=
−
3
The graph itself will look like this:
graph{abs(-x+3)-4 [-10, 10, -5, 5]}