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

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13-09-2017
Mathematics

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

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danielmaduroh danielmaduroh · Answer 1 · 2018-09-14T22:10:13+02:00

The graph of [tex]f(x)=x^2[/tex] and the graph of [tex]g(x)=(x-5)^2+1[/tex]. These two graphs are illustrated in the Figure bellow. So, let's explain what this means:

For a function f(x), a new function g(x) = f(x - c) represents to shift the graph c units to the right.
For a function f(x), a new function g(x) = f(x) + k represents to shift the graph k units upward.

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.

facundo3141592 facundo3141592 · Answer 2 · 2022-02-21T13:59:42+01:00

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

How do translations work?

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.

If N is positive, then the shift is upwards.
If N is negative, then the shift is downwards.

Horizontal translation:

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

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

If N is positive, then the shift is to the left.
If N is negative, then the shift is to the right.

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:

https://brainly.com/question/17485121