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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.

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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.
isyllus

Answer:

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

A is correct.

Step-by-step explanation:

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

Parent Function:

[tex]f(x)=\log_4x[/tex]

Now we shift 2 unit right [tex]x\rightarrow x-2[/tex]

[tex]f(x)=\log_4(x-2)[/tex]

Now we shift 4 unit up [tex]f(x)\rightarrow f(x)+4[/tex]

[tex]g(x)=\log_4(x-2)+4[/tex]

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.

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