Question

7 multiple choice 1 point which of the following is a function?

Explanation:

Step1: Recall vertical - line test

A relation is a function if for every \(x\) - value there is exactly one \(y\) - value. The vertical - line test states that if any vertical line intersects the graph of a relation at more than one point, the relation is not a function.

Step2: Analyze first graph

The first graph is a vertical line. A vertical line has the equation \(x = a\) (where \(a\) is a constant). For a vertical line, there are infinitely many \(y\) - values for a single \(x\) - value. So, it is not a function.

Step3: Analyze second graph

The second graph is a circle. For most \(x\) - values within the domain of the circle, there are two \(y\) - values (one above and one below the \(x\) - axis). For example, if the circle is centered at the origin with radius \(r\), the equation is \(x^{2}+y^{2}=r^{2}\), and solving for \(y\) gives \(y=\pm\sqrt{r^{2}-x^{2}}\). So, it is not a function.

Step4: Analyze third graph

The third graph is a parabola opening to the right with the equation of the form \(x = ay^{2}+by + c\). For most \(x\) - values in its domain, there are two \(y\) - values (one on the upper - part and one on the lower - part of the parabola). So, it is not a function.

Since no correct option is shown in the problem - statement as presented (assuming these are the only options), we cannot provide a valid answer from the given choices. If we had to choose based on the principle of the vertical - line test, none of the above graphs represent a function. But if we assume there was an un - shown correct graph that passes the vertical - line test, we would need to see it to give a proper answer.

If we assume this was a mis - presentation and we were to correct it, a graph of a non - vertical line (e.g., \(y=mx + b\)), a parabola opening up or down (e.g., \(y = ax^{2}+bx + c\)), etc. would be a function as they pass the vertical - line test.

If we assume this was a multiple - choice with no correct option shown:

Answer:

None of the above

If we assume there was a correct option not shown and we consider the general form of functions: A graph of a linear function \(y = mx + b\) (where \(m\) and \(b\) are constants and \(m
eq0\)) or a quadratic function \(y=ax^{2}+bx + c\) (\(a
eq0\)) opening up or down would be a function as they pass the vertical - line test. But without a correct option shown in the given problem, we stick with "None of the above".