Question

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What are the domain and the range of this graph?
(A) The domain is x ∈ R and the range is y ∈ R.
(B) The domain is x ∈ R and the range is y ∈ R.
(C) The domain is x ≥ −1 and the range is y ∈ R.
(D) The domain is x ∈ R and the range is y ∈ R.

Answer 1

B

Explanation:

Answer 2

B

Explanation:

The domain is the span of x-values covered by the graph, while the range is the span of y-values covered by the graph.

DOMAIN:

From the graph, we can see that the span of x-values covered will be all real numbers. This is because the graph will stretch infinitely in both directions (as indicated by the arrows at the end of the graph), thereby covering all x-values.

So, the domain is all real numbers. In set notation, this is:

`\{x|x\in \mathbb{R}\}`

RANGE:

We can see that the span of y-values will always be greater than or equal to -1. This is because the lowest point of the graph is y=-1. The graph will never go below this point. However, it will extend infinitely upwards from this point.

So, our range is all real numbers greater than or equal to -1. In set notation, this is (and we use y because this describes the range):

`\{y\in\mathbb{R}\ |y\geq -1}\}`

Therefore, our answer is B.