Question

Pls answer

100 points!
what is the effect on the graph of the function f(x)= x^2 when f(x) is changed to f( x - 6)

Shifted up
shifted left
shifted right
shifted down

Answer 1

Find shift

f(x-6)

• (x-6)²

So

• f(x)=x²

x is decreased 6 units

So

The graph will shift 6 units right

Graph attached

Answer 2

shifted right

Explanation:

Translations

For
`a > 0`

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

Parent function:
`f(x)=x^2`

Translated 6 units to the right:
`f(x-6)=(x-6)^2`