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Find $g(x)$ , where $g(x)$ is the translation $4$ 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

4

units up of

f(x)=x

. Write your answer in the form

mx+b

, where

m

and

b

are integers.

Identify Rule: Identify the translation rule for moving a function up by $k$ units.
Translate Function Up: To translate $f(x) = x$ up by $4$ units, we add $4$ to $f(x)$ .
New Function: So, $g(x) = f(x) + 4$ .
Substitute $x$ : Since $f(x) = x$ , substitute $x$ into the equation.
Final Function: $g(x) = x + 4$ .

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