Math

QuestionStretch the function f(x)=3x+9f(x)=3x+9 horizontally by a factor of 4.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=3x+9f(x)=3x+9 . We are applying a horizontal stretch by a factor of4

STEP 2

The general form of a horizontal stretch for a function f(x)f(x) by a factor of kk is f(kx)f(kx). So, we need to replace every xx in the original function with kxkx.

STEP 3

Substitute kxkx for xx in the original function f(x)f(x), where kk is the stretch factor.
f(kx)=3(kx)+9f(kx) =3(kx) +9

STEP 4

Now, plug in the given value for the stretch factor kk to calculate the stretched function.
f(4x)=3(4x)+9f(4x) =3(4x) +9

STEP 5

implify the function.
f(4x)=12x+9f(4x) =12x +9The function f(x)=3x+9f(x)=3x+9 after a horizontal stretch by a factor of4 is f(4x)=12x+9f(4x)=12x+9.

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