Question

find g(x), where g(x) is the translation 4 units left and 5 units up of f(x) = x. write your answer in the form mx + b, where m and b are integers. g(x) =

Explanation:

Step1: Apply horizontal - shift rule

For a function $y = f(x)$, a translation $a$ units to the left gives $y=f(x + a)$. Here $a = 4$ and $f(x)=x$, so after the 4 - unit left - shift, the function becomes $y=(x + 4)$.

Step2: Apply vertical - shift rule

For a function $y = f(x)$, a translation $b$ units up gives $y=f(x)+b$. Here $b = 5$, and the function after the left - shift is $y=(x + 4)$. So after the 5 - unit up - shift, the function $g(x)=(x + 4)+5$.

Step3: Simplify the expression

$g(x)=x+4 + 5=x + 9$.

Answer:

$g(x)=x + 9$