Question

Kendra drew the graph of G(x). She noticed that it was possible to draw a horizontal line that intersected the graph in two points. Which best describes what that means?

A. The inverse of G(x) is not a function.
B. The inverse of G(x) is a function.
C. G(x) is a function.
D. G(x) is not a function.

Answer 1

C. if it had been a vertical line that passes through two points G(x) would not have been a function as the same input would give two different outputs.

Note, however, that the horizontal line would have the same y-value at both the x-values and that is absolutely okay because two different inputs can have the same output.

Basically, it is easy to see with this => y = x^2 now for x = -2; y = 4 and for x = 2; y = 4. Everything is mathematically sound when two different inputs give the same input.

But, to say the same input could give two different outputs is bogus => y = x + 3 where x = 4; y = 7 and where x = 5; y = 7. Pretty obvious something's wrong :)

Just realised that while what I said above is true... it is not the most relevant. Here's why.

For a function to have an inverse function the function need to be one-one and an easy way to test this is to see if a horizontal will cut two points on the graph for any y-value.

So, A. The inverse of G(x) is not a function.

Answer 2

A is correct