Question

F(x)=x^2
g(x) = (x– 9)^2 +3
We can think of g as a translated (shifted) version of f.

Answer 1

To get the function g, shift f up by 3 units and to the right by 9 units.

Explanation:

Answer 2

To get the function g, shift f up by 3 units and to the right by 9 units.

Explanation:

The given functions are

`f(x)=x^2`

`g(x)=(x-9)^2+3`

If f(x) is a parent function, then g(x) can be written in the form of f(x) as

`g(x)=f(x-9)+3` ...(1)

The translation is defined as

`g(x)=f(x+a)2+b` ... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

`a=-9,b=3`

It means, to get the function g, shift f up by 3 units and to the right by 9 units.