Question

1.

For the function whose graph is shown, which is the correct formula for the function?


A. y = |x + 1|

B. y = |x| + 1

C. y = |x| – 1

D. y = |x – 1|

Answer 1

C. y = |x| - 1

Explanation:

y = |x| Is the same graph, but with the vertex on point (0,0)

y = |x+1| Moves graph to the left 1

y = |x| + 1 Moves the graph up 1

y = |x| - 1 moves the graph down 1

y = |x-1| moves the graph right one

Therefore, y = |x| - 1 is the answer.

To further explain it, you can write down a table of values for proof. For y = |x| when x = 0, y = 0. When x = 1, y = 1 and so on. When x = -1, y = 1 and so on in that direction.

If we look at the choices and plug in numbers, we get for A when x = 0, y = 1, which if we look at the graph given does not fit.

For B, when x = 0, we get y = 1, which again does not work.

For C, when x = 0, y = -1, which is the answer we need, but to make sure, I am going to do D.

For D, when x = 0, y = 1. Therefore, C is the only possible answer.

Answer 2

y = |x| - 1

Explanation:

The difference between the parent function (y=|x|) and the graph, is that the graph is 1 unit down. y = |x| -1 has the parent function 1 unit down