Question

Which of the following tables represents a linear function?

x −2 −1 0 1 2
y 4 1 −2 −5 −8

x −2 −1 0 1 2
y 4 1 0 1 4

x 2 2 0 2 2
y −2 −1 0 1 2

x 0 1 2 3 4
y −2 1 0 1 −2

Answer 1

Explanation:

answer A

Answer 2

A, B, D

Explanation:

A linear function has one input per output. This means one input (x) cannot have two different outputs (y); however, two different inputs (x) can have the SAME output.

This premise is what leads us to the "vertical line test". If we were to plot out all of our points on a graph and then connect a line to each point, we'd graph our function. If we held up a vertical line to ANY place on that graph, we should never have any part of the graph cross this paper more than once on the same line.

For example, a horizontal line would pass the vertical line test. Anywhere we hold up out vertical line, our horizontal line only crosses it once.

Meanwhile, a circle would fail the vertical line test. A circle would cross our vertical line at TWO different places for the same x-value, which makes it an equation, not a function.

Knowing this, we know we must never have two different y-values assigned to the same x value.

If you list your answers in order as A, B, C, & D, only graphs of A, B, and D pass. C does not pass because there are numerous instances of the input "2" having different y-values, meaning it'd cross our vertical line at this point multiple times and fail.