Question

Which equation does not represent a function? A) y = 2x + 3 B) x = 4y + 7 C) 6x - 5y = 8 D) y2 = -5x - 8

Answer 1

D. It is not a function because there are multiple outputs for one input. 

Answer 2

D) y2 = -5x - 8

Explanation:

A function is a rule between two sets A and B so that each element of set A (Domain) corresponds to a single element of set B (Range). Mathematically they can be expressed as:

`f: A\rightarrow B\\\\a\rightarrow b =f(a)`

So:

`y^2=-5x-8\\\\y=\pm √(-5x-8)`

Isn't a function because the elements of the domain don't corresponds to a single element of the range.

We can see this in an easier way using the vertical line test, which is a visual way to determine if a curve is a graph of a function or not. If a vertical line intersects a curve in an xy plane more than once, then for a value of x the curve has more than one value of y, and then the curve does not represent a function.

I attached you the graphs, so you can corroborate the results visually.