Question

Find the domain and range of the relation and determine whether it is a function.

(1 point)
Responses

domain: positive integers; range: positive integers; No, it is not a function.

domain: x ≥ 0; range: y > –2; No, it is not a function.

domain: all real numbers; range: all real numbers; Yes, it is a function.

domain: x > –2; range: y > 0; Yes, it is a function.

Answer 1

Answer: D

Step-by-step explanation: First off, we can use the Vertical Line Test to determine if this graph represents a function.

The vertical line test is a method used to determine if a graph represents a function by checking if any vertical line intersects the graph at more than one point.

Here, it's impossible to draw a vertical line that intersects more than one point on the graph, so we know this must be a function.

Secondly, let's find the domain and range. The domain is all the possible x-values and the range is all our possible y-values.

On this graph here, notice that x can be anything but we have an asymptote at x = -2 so we can't go any further to the left.

So our domain would be {x: x > -2}.

Our range would be all our y-values and looking at the graph, notice that we don't seem to go below y = 0 but we go up indefinitely.

So our range would be {y: y > 0}.

So our answer therefore would be D.