Question

Which statements describe one of the transformations performed on f(x) = x2
to create g(x)= 3(x+ 5)2 -2 ? Choose all that apply.

Answer 1

Given:

The given functions are:

$f(x)=x^2$

$g(x)=3(x+5)^2-2$

To find:

The transformations performed of f(x) to create g(x).

Solution:

The translation is defined as

$g(x)=kf(x+a)+b$                .... (i)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

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.

We have,

$f(x)=x^2$

$g(x)=3(x+5)^2-2$

Using these two function, we get

$g(x)=3f(x+5)-2$                 ...(ii)

On comparing (i) and (ii), we get

$k=3,a=5,b=-2$

It means the graph of f(x) is vertically stretched with a scale factor of 3, shifts 5 units left and 2 units down to get g(x).

Therefore, the correct options are A and C.