How do you know a relation is a function?

1.) A function can't have any repeated x-coordinates

For example:

{(3, 4), (3, 6), (5, 4)}

This is not a function because 3 is repeated.

{(2, 1) (4, 1), (5, 1)}

This is a function because the y-coordinates can be the same, but not the x-coordinates.

2.) When a function is graphed, it will only have one intersection point with a vertical line.

For examples, see the image attached.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

irrational, cannot