Question

The graph of y = |x| is the solid black graph below. Which

function represents the dotted graph?
A.y=(x-1)-3
B.y=(x+1)-3
C.y=(x-1)+3
D.y=(x+1)+3

Answer 1

A function represents the dotted graph include the following: D.y = |x+1|+3.

In Mathematics, the vertex form of the equation for an absolute value function can be modeled by the following:

y = a|x - h| +k.

Where:

• h and k are the vertex of the graph.
• a is a numerical constant.

By critically observing the graph of the absolute value function, we can logically deduce that the parent absolute value function y = |x| was horizontally shifted to the right by 1 unit and vertically shifted by 3 units up, in order to produce the dotted graph as follows;

y = a|x - h| +k.

y = |x + 1| + 3