Question

Hey,

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

f(x) = blank, x < or equal to blank

g(x) = blank, x greater than blank

Answer 1

The absolute value is defined as

`|x| = \begin{cases}x \text{ if } x\geq 0\\-x \text{ if } x < 0\end{cases}`

In your case, the expression inside the absolute value is
`x-3`, which changes sign at
`x=3`. So, you have

`2|x-3|+5 = \begin{cases}2(x-3)+5 \text{ if } x\geq 3\\2(3-x)+5 \text{ if } x < 3\end{cases}`