Question

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

Which of the following statements describe the graph of
? Select three that apply.

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A.
The vertex is located at
.

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B.
There is a y-intercept located at
.

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C.
There is a y-intercept located at
.

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D.
There is an x-intercept located at
.

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E.
There is an x-intercept located at
.

Answer 1

Compute values:
- Vertex: y = |x+3| - 1 has its corner where x+3 = 0, so x = -3 and y = -1. Vertex: (-3, -1).
- y‑intercept: plug x = 0 → y = |0+3|-1 = 3-1 = 2. y‑intercept: (0, 2).
- x‑intercepts: set |x+3|-1 = 0 → |x+3| = 1 → x+3 = ±1 → x = -2 or x = -4. x‑intercepts: (-2, 0) and (-4, 0).

So mark the choices that match these points (the option giving (-3,-1), the option giving (0,2), and the option(s) giving (-2,0) and (-4,0)).