Question

Which answer describes the transformation of g(x)=log4(x−2)+4 from the parent function f(x)=log4x?

It is the graph of f(x) shifted 2 units right and 4 units up. It is the graph of f(x) shifted 2 units left and 4 units down. It is the graph of f(x) shifted 4 units left and 2 units down.

Answer 1

The correct answer for this question is this one: "A. It is the graph of f(x) shifted 2 units right and 4 units up."

The choices are the following:
A. It is the graph of f(x) shifted 2 units right and 4 units up.
B. It is the graph of f(x) shifted 2 units left and 4 units down.
C. It is the graph of f(x) shifted 4 units left and 2 units down.

Answer 2

It is the graph of f(x) shifted 2 units right and 4 units up.

A is correct.

Explanation:

We are given two function. One is parent function and another is transform using shifting.

Parent Function:

`f(x)=\log_4x`

Now we shift 2 unit right
`x\rightarrow x-2`

`f(x)=\log_4(x-2)`

Now we shift 4 unit up
`f(x)\rightarrow f(x)+4`

`g(x)=\log_4(x-2)+4`

We changed f(x) to g(x) by two transformation

• f(x) shifted 2 unit right then
• f(x) shifted 4 unit up

Thus, we get g(x) by transform of f(x) shifted 2 unit right and shifted 4 unit up.