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Find $g(x)$ , where $g(x)$ is the translation $10$ units up of $f(x) = x$ . Write your answer in the form $mx + b$ , where $m$ and $b$ are integers.

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Transformations of linear functions

Full solution

Q. Find

g(x)

, where

g(x)

is the translation

10

units up of

f(x) = x

. Write your answer in the form

mx + b

, where

m

and

b

are integers.

Identify $g(x)$ : Identify $g(x)$ when translating $k$ units up of $f(x)$ . Transformation rule: $g(x) = f(x) + k$
Translate $10$ units up: Identify $g(x)$ when translating $10$ units up of $f(x)$ . Substitute $10$ for $k$ in $g(x) = f(x) + k$ . $g(x) = f(x) + 10$
Write function $g(x)$ : We have:
$f(x) = x$
$g(x) = f(x) + 10$
Write the function $g(x)$ .
Substitute $x$ for $f(x)$ in $g(x) = f(x) + 10$ .
$g(x) = x + 10$

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