Question

Which transformation of f(x) will produce the same graph as g(x)?

Answer 1

g(x) =f(x) +3

given f(x) =3x

i.e. g(x) =3x+3

For F(x) to be same as g(x)

3 must be added to f(x)

i.e. h(x) =3x+3

->h(x)= 3x +3(1)

-> h(x) = f(x) +f(1)

-> h(x) =f(x+1)

Hence Option (a) is your answer...

Hope it helps...

Regards

Leukonov/Olegion

Answer 2

A) h(x) = f(x +1).

Explanation:

Given : f(x) = 3x and g(x) = 3x + 3.

To find : Which transformation of f(x) will produce the same graph as g(x).

Solution : We have given

f(x) = 3x

For x = 1.

f(1) = 3 (1)

f(x) = 3.

Plug the value of f(x) =3x and f(1) = 3 in g(x).

g(x) = 3x + 3.

g(x) = f(x) + f(1).

We can write f(x) + f(1) = f(x +1).

g(x) = f(x +1)

h(x) = f(x +1)

So, it is a new function produce the same graph as g(x).

h(x) = f(x +1).

Therefore, A) h(x) = f(x +1).