Question

Rewrite the equation y=2|x−3|+5 as two linear functions f and g with restricted domains.

Please help

Answer 1

f(x) = 2+5

g(x) = 2(-(x−3))+5

Explanation:

If you remember, an absolute value can have two different answer, a positive and negative answer because the absolute value symbol makes all values in it positive. Example: |-2|=2 and |2|=2

So if y = 2|x−3|+5

then the two possibilities are

y = 2(x−3)+5 and

y = 2(-)+5

Set one of them equal to f(x) and the other one to g(x)

f(x) = 2(x−3)+5

g(x) = 2(-(x−3))+5

You can also write it as a piecewise function.

`y(x)=$\begin{array}{cc} \{ & \begin{array}{cc} -(x-3) & x<3 \\ 0 & x=3 \\ (x-3) &x>3 \end{array}\end{array}$`