Question

Consider the function
ƒ
(
x
)
=
|
x
+
3
|
−
1
.

Which of the following statements describe the graph of
f
(
x
)
? Select THREE that apply.


The vertex is located at
(
−
3
,
−
1
)
.


There is a y-intercept located at
(
0
,
−
2
)
.


There is a y-intercept located at
(
0
,
2
)
.


There is an x-intercept located at
(
2
,
0
)
.


There is an x-intercept located at
(
−
4
,
0
)
.

Answer 1

Correct statements (three):

- The vertex is located at (−3, −1). (f(−3)=|−3+3|−1=−1.)
- There is a y-intercept located at (0, 2). (f(0)=|0+3|−1=3−1=2.)
- There is an x-intercept located at (−4, 0). (Solve |x+3|−1=0 ⇒ |x+3|=1 ⇒ x+3=±1 ⇒ x=−4 or x=−2; −4 is listed.)

Incorrect: (0, −2) and (2, 0).