Which transformations to the graph of j(x) would result in the graph of j(4x) – 27? A) horizontal stretch by a factor of 4, and a translation 27 units right
B) horizontal stretch by a factor of 4, and a translation 27 units down
C) horizontal compression by a factor of 4, and a translation 27 units right
D)horizontal compression by a factor of , and a translation 27 units down

Option D.

Step-by-step explanation:

It is given that, graph of j(x) transformed in the graph of j(4x) – 27.

We need to find the transformations.

Consider the new function is

         ... (1)

The translation is defined as

               ... (2)

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

If 0<k<1, then the graph stretched horizontally by factor of 1/k and if k>1, then the graph compressed horizontally by factor of 1/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.

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

k=4>1, the graph j(x) compressed horizontally by factor of 1/4.

a=0, so there is no horizontal shift.

b=-27<0, so the graph of j(x) shifts 27 units down.

So, the required transformations are horizontal compression by a factor of 1/4, and a translation 27 units down.

Therefore, the correct option is D.

14

step-by-step explanation:

14 x 3 = 42