Question

If g(x)=2x were shifted 5 units to the right and 2 units downs, what would the new equation be?

Answer 1

The new equation would be
`h(x) = 2x - 12`

Explanation:

Shifting a function f(x) a units to the right is doing the following operation:

`f(x) = f(x-a)`

Shifting a function f(x) a units down is doing the following operation:

`f(x) = f(x) - a`

In this question:

`g(x) = 2x`

Shifting 5 units to the right:

`g(x-5) = 2(x-5) = 2x - 10`

Shifting 2 units down:

`g(x-5) - 2 = 2x - 10 - 2 = 2x - 12`

The new equation would be
`h(x) = 2x - 12`