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
