Question

Evaluate the piecewise function

Answer 1

f(-3)=-1

f(4)=7

f(-1)=-3

f(12) = -24

Explanation:

Piecewise Functions

The piecewise functions define different pieces or subfunctions where the domain is divided into parts according to some conditions on the independent variable.

The pieces of the function are defined as shown below:

`f(x)=\left\{\begin{matrix}-1 &x\le -2\\ 2x-1 &-2<x\le 4 \\ -3x+8 &x>4 \end{matrix}\right.`

Let's find the values of:

f(-3). Here the variable x is -3. We have to find the interval where x=-3 belongs. Since -3 ≤ -2:

f(-3)=-1

f(4). The variable x is 4 and it belongs to the second interval, thus

f(4)=2*4-1=7

f(4)=7

f(-1). x = -1. It belongs to the second interval, thus:

f(-1)=2*(-1)-1=-3

f(-1)=-3

f(12). x=12 belongs to the last interval since 12 > 4, thus:

f(12)= -3*12+8 = -36 + 8 = -24

f(12) = -24