Question

The graph of y = |x| is shifted down by 9 units and to the right by 4 units. What is the equation of the new graph?

Answer 1

Answer:

The equation of the new graph is y = |x - 4| - 9

Step-by-step explanation:

Given

Graph of y = |x|

Shifted down by 9 units

Shifted right by 4 units

Required

New equation of the graph

Basic points to note

1. When you shift a point in the down or right direction, it attracts a "-" operation.

When the point is shifted otherwise, it means the point is decrement and it attracts a "+".

2. When you shift a point up or down, the shifted point is added or subtracted outside the basic function

If otherwise, the shifted point is added or subtracted inside the function argument.

Having mentioned these, we proceed by first analysing the graph equation

y = |x|

The first condition states that the graph is shifted down by 9 units

Being shifted "down" means that a "-" operation will be done outside the basic function

The new equation becomes

y = |x| - 9

The second condition states that the condition is then shifted to the right by 4 units.

Being shifted "right" means that a "-" operation will be done inside the function argument

Represent the function argument by f(x)

so,

f(x) = |x| - 9

Recall that the 4 will be subtracted from the function argument.

The function argument becomes

f(x - 4)

The new equation becomes

f(x - 4) = |x -4| - 9

y = |x- 4| - 9