Question

The graph of y = 2 is shifted down by 6 units and to the left by 9 units.

What is the equation of the new graph?
Choose 1 answer:
A
y=|x + 9 |+ 6
B
y =|x +9| – 6
C y = |2 - 9|+6
D y = |2 - 9|– 6

Answer 1

`y = |x + 9| - 6`

Explanation:

Given

`y = |x|` --- the correct equation

Shifted down 6 units

Shifted left 9 units

Required

The new equation

When function is shifted down by b units, the new function is:

`(x,y) = (x,y-b)`

In this case:

`b =6`

So,
`y = |x|` becomes

`y =|x| - 6`

When function is shifted left by b units, the new function is:

`(x,y) = (x+b,y)`

In this case:

`b =9`

So:
`y =|x| - 6` becomes

`y = |x + 9| - 6`