Question

Please someone explain how to solve this piecewise function!!!! Im super confused

Answer 1

From top to bottom:

`0, 1, 2, -8, -8`

Explanation:

We are given the piecewise function:

`g(x) = \left\{ \begin{array}{ll} 0.5x+1 & \text{if } x \leq 2 \\ -8 & \text{if } x > 2 \end{array} \right.`

Row 1:

We want to find g(-2).

Since -2 is less than (or equal to) 2, we will use the first equation. Thus:

`g(-2)=0.5(-2)+1=-1+1=0`

Row 2:

Likewise, 0 is less than or equal to 2. We will continue to use the first equation:

`g(0)=0.5(0)+1=1`

Row 3:

2 is not less than 2 but it is equal to 2. So we will continue to use the first equation:

`g(2)=0.5(2)+1=1+1=2`

Row 4 and 5:

Both 4 and 6 are greater than 2. Thus, we will use the second equation. Therefore:

`g(4)=-8\text{ and } g(6)=-8`