Question

Express the function graphed on the axes below as a piecewise function.108642-10-8-6-4-22416810-4-6-8-10

Answer 1

`f(x)=\begin{cases}2x+3,x\le-4 \\ 2x-12,x>2\end{cases}`

Step-by-step explanation:

The equation of the line to the left is 2x + 3 and we see that it only exists for x <= -4.

The equation of the line to the right is 2x - 12 and we see that it only exists for x > 2.

Therefore, we can write

f(x) = 2x + 3 for x < = -4

f(x) = 2x -12 for x > 2

Or in the notation of piecewise function, the above can be written consicely as

`f(x)=\begin{cases}2x+3,x\le-4 \\ 2x-12,x>2\end{cases}`

which is our answer!