Question

Let f(x)=−3x. The graph of f(x) ​is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
What is the equation for g(x) ?



Enter your answer in the box.

g(x)= ___________


The graph of the function f(x)=|3x| is translated 4 units up.

What is the equation of the transformed function?



Enter your answer in the box.


g(x)= ___________

Answer 1

Answer:

Ques 1)

                   $g(x)=-12x+48$

Ques 2)

                 $g(x)=|3x|+4$

Step-by-step explanation:

Ques 1)

We know that if a graph is stretched by a factor of a then the transformation if given by:

    f(x) → a f(x)

Also, we know that the translation of a function k units to the right or to the left is given by:

  f(x) →  f(x+k)

where if k>0 then the shift is k units to the left

and if k<0 then the shift is k units to the right.

Here the graph of f(x) ​is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.

This means that the function g(x) is given by:

$g(x)=4f(x-4)\\\\i.e.\\\\g(x)=4(-3(x-4))\\\\i.e.\\\\g(x)=-12(x-4)\\\\i.e.\\\\g(x)=-12x+48$

Ques 2)

We know that the transformation of the type:

  f(x) → f(x)+k

is a shift or translation of the function k units up or down depending on k.

If k>0 then the shift is k units up.

and if k<0 then the shift is k units down.

Here, The graph of the function f(x)=|3x| is translated 4 units up.

This means that the transformed function g(x) is given by:

                 $g(x)=|3x|+4$