Answer:
Step-by-step explanation:
Refer to the definition of a function. I'll just give you a layman's definition to be concise.
For something to be a function, there needs to be exactly 1 output for every input. You cannot have a case where you input 1 value, and get 2 or more values as an output.
In math we call all the possible input values the domain, and we call all the possible output values the range.
Let's take a look at each situation on your worksheet.
1. Is a function. This is because only one arrow stems from each input value. There are cases where the different input values give the same output, sure, but each input returns 1 discrete thing, not an array of things.
(Think of it this way, if i had a machine that could answer any question I had with yes, no or maybe. I wouldn't want the machine to give me "yes and maybe" or "yes and no" as the result when I ask it a question. That doesn't make sense and I would think the machine is broken. What could happen, is that I ask the machine different questions, and for those different questions, it gave me the same answer, like "yes" and "yes" respectively. in that case, it would be acceptable, because it isn't contradicting itself for any individual question.)
2. Not a function. There are 2 different output values for b.
(Refer back to my machine analogy. The "machine" in this question is contradicting itself. I gave the machine one input, and the machine is telling me, "it's this and actually it's this other thing too")
3. Is a function for the same reasons as 1.
4. Isn't a function.
(It's basically telling you, the machine reads -6 as -4, but it also reads -6 as 0, and also 2. And it also tells you the machine reads -4 as -3, but it also reads it as 8. Again, the machine should only read 1 input in 1 way and not contradict itself. )
