Question

If you could help I would really appreciate it, but if not that’s fine. Thank you.

Answer 1

Option C is correct answer.

Explanation:

We need to draw the graph of piece wise function

`f(x)\[ \begin{cases} -2-x & if\:x\leq 1 \\ -3+2x & if\: x>1 \end{cases}\]`

So, for drawing the graph, we will find values of f(x) for both the given equations.

First finding f(x) for
`-2-x \:\: if\:x\leq1`

The value of x must be less than or equal 1

x f(x)

1 -3

0 -2

-1 -1

-2 0

-3 1

-4 2

The graph will start from closed circle because x ≤ 1

Now, finding values of f(x) for
`-3+2x\: if\:x>1`

The value of x must be greater than 1

x f(x)

2 1

3 3

4 5

5 7

The graph will start from open circle because x> 1

Now, plotting these numbers we will get graph of Option C.

Option C is correct answer.