Which of the following is true regarding the image shown?

B) It is a relation and is NOT a function

Explanation:

We don't have a function because it is possible to draw a single straight vertical line through more than one point on the curve. This graph is said to fail the vertical line test. A function is only possible if any x input leads to exactly one y output, but that's not the case here (eg: x = 0 leads to three different y values). So there are many approaches to see why we don't have a function.

It is a relation however because any relation is simply a collection of (x,y) points; often this collection forms some sort of rule or pattern though it's not mandatory. A graph is a visual way to represent (x,y) points. Some graphs are connected (continuous) with a curve, or other graphs are a set of discrete points, or they may be a mix of both varieties.

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are