The graph of f(x) = x2 is translated to form g(x) = (x – 5)2  + 1.which graph represents g(x)?

The graph of and the graph of . These two graphs are illustrated in the Figure bellow. So, let's explain what this means:

Since in our problem the function g(x) = f(x - c) + k, we have shifted the function f(x) c units to the right and k units upward, that is, we have shifted the function f(x) 5 units to the right and 1 unit upward as indicated in the Figure bellow.

The graph of the original function and the translated function can be seen at the end of the answer.

There are two types of translations:

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

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

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

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

Then if we go from:

f(x) = x^2

to:

g(x) = (x - 5)^2 + 1

Then we have a translation of 5 units to the right and one unit upwards.

The graph can be seen below.

If you want to learn more about translations, you can read:

link

here is the

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step-by-step explanation: