Function? Correspondence? Neither?-cont.

[Kinetica]

Homework Statement

Consider the following mathematical items.
For each item, (1) indicate whether it has a natural interpretation as a function, a correspondence, or neither. If the item is a function or a correspondence, the indicate (2) its domain and range and (3) whether it is (a) real, (b) single-valued and (c) univariate.
If the item is not a function, or is not real, single-valued or univariate, then justify your answer briefly.

The Attempt at a Solution

6. (x,y): y=f(x), f(x)=x², -1=<x=<1. This is a function, Domain (-1=<x=<1 ), Range (infinity), real/single-valued/univariate? how to tell?

7. (x,y): y=f(x), f(x)=x^1/2, -1=<x=<1. My teacher told that this is NOT a function, and I don't get why. Is it correspondence? How do you tell? real/single-valued/univariate?

8. And a tough one, that needs to be plotted;

(x,y): y=f(x), f(x)=(i-1)+x if i is odd
f(x)=(i-x if i is even, i=1, 2...,.. 0=<x=<1

 

[annoymage]

The Attempt at a Solution

6. (x,y): y=f(x), f(x)=x², -1=<x=<1. This is a function, Domain (-1=<x=<1 ), Range (infinity), real/single-valued/univariate? how to tell?

7. (x,y): y=f(x), f(x)=x^1/2, -1=<x=<1. My teacher told that this is NOT a function, and I don't get why. Is it correspondence? How do you tell? real/single-valued/univariate?

hmm how about, you wrote here the definition of

a) a function
b) correspondence
c) real
d) single
e) univariate

the definition is very important, so maybe we can help you understand it