Answer:
0
Step-by-step explanation:
Piecewise functions are like recycling bins. They give you a piece of information for whatever value you may encounter on your graph. So, all you need to do is sort out the value they give you into the correct "bin," so to speak.
The first equation they give you is for any value less than zero. So, anything from -0.9999999 (you get the idea) onwards will use the equation on the right. So, if you have a value less than zero, then you will plug the x-value into the equation (-x - 2). Therefore, let's say your value was f(-1). You'd do: (-(-1) - 2). The negative cancel on your -1 and you're left with 1. Then, 1 - 2 = -1. So, in this example, your answer would be f(-1) = -1.
The second equation gives you a possible range for any numbers between zero and anything less than three. Notice how in this one, the zero is included. This is because when you actually go to draw a piecewise function, your values can't repeat, or else it wouldn't be a function. So, since the problem asks you to find f(0), you need to use the second equation since it is the one that includes zero in its possible values. Thus, you plug in your number. In this case, the number is 0, so x = 0. The answer is to f(0) = 0
Lastly, the third equation is for any values that are three or bigger. This one includes the three in its possible values. If they gave you a value like f(4), you just do the same as in the last examples. 4^2 - 1 = 15. So, f(4) = 15.
And that's all there is to it. Just plug in the value they give you into the appropriate equation, and you'll be good to go. Hope this helped!
