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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.

Which Statements Describe One Of The Transformations Performed On Fx X2 To Create Gx 3x 52 2 Choose All That Apply class=

Sagot :

Given:

The given functions are:

[tex]f(x)=x^2[/tex]

[tex]g(x)=3(x+5)^2-2[/tex]

To find:

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

Solution:

The translation is defined as

[tex]g(x)=kf(x+a)+b[/tex]                .... (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,

[tex]f(x)=x^2[/tex]

[tex]g(x)=3(x+5)^2-2[/tex]

Using these two function, we get

[tex]g(x)=3f(x+5)-2[/tex]                 ...(ii)

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

[tex]k=3,a=5,b=-2[/tex]

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.

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