a A graph is a function if no values of x give multiple values of y. We can investigate this by performing a Vertical Line Test. That is, if we draw a vertical line anywhere in the coordinate plane,it can only intercept the graph once if it is a function. Let's try this with an arbitrary vertical line.
As we can see, the vertical line only intersect the graph once. We would get the same result no matter how we drew the line. This means this graph does indeed represent a function.
b Like in Part A, we will perform a Vertical Line Test.
As we can see, the graph failed the test since we have two points of intersections. This means it is not a function.
c Like in previous parts, we will perform a Vertical Line Test.
As we can see, the vertical line only intersects the graph once. We would get the same result no matter how we drew the line. This means this graph does indeed represent a function.
d In this case we have a vertical line. Such a graph would definitely fail the Vertical Line Test since, well, it is a vertical line. Therefore, this is not a function.
e Part A shows a constant function. No matter what value of x we have, the function will always produce the same y-value: in this case y=2. Below we see a few examples.
