Consider the following: h={(1,2),(2,4),(3,6),(-1,-2),(-2,-4)}.
a) Explain why h: ℤ --> ℤ does not describe h correctly.
This does not describe the function h correctly because the range of the function h seems to be finite or limited to the set of even integers while the codomain of function h is the set of integers. Since these two aren't equal to each other, then we can't say that h is a function from the set of integers to the set of integers. Is this the correct answer?
b) If the co-domain of h is the set {-4, -2, 0, 2, 4,... , 6}, is h onto? Why or why not?
If the co-domain of h is the set given, then this function would not be onto because the range of h is not equal to the codomain given. While each input goes to exactly one input, implying that it is one to one, this function is not onto because not every single element in the codomain was met. Is this a good explanation?