Question

How do you know if y=3x-2 is a function?

Answer 1

As long as the X's don't repeat

Explanation:

Draw the equation out on a graph, and copy down the X values for each plotted point. As long as none of the X values repeat, it is a function. If there is a repeated X, but it is negative while the other one is positive, it is still a function; the X's would have to be exactly the same to negate a function. graph{y=3x-2 [-10, 10, -5, 5]}

Answer 2

y=3x-2 is a function because it passes the vertical line test.

Explanation:

We use the vertical line test on a graph to determine whether it is a function or not. Because a function is defined as a relation where there is exactly one value for each value of y, if there are multiple values of y for an x value the relation will fail the test.

Because a vertical line drawn through the function y=3x-2 at any point will only intersect the graph at one point, it is a function.

graph{3x-2 [-10, 10, -5, 5]}