To determine if a relation is a function, ask one very important question:
does the relation satisfy the one-to-one condition? That is to say does the relation maps to two values in the codomain (range) from one value in the domain?
Examples:
f(x)=sqrt(x) is not a function because sqrt(x) results in two values.
f(x)=any polynomial with real (i.e. not complex) coefficients is a function, because polynomials satisfy the ono-to-one requirement.
Now can you pick out the functions from the above list, and state why the other(s) is not?
5. Which of the following are functions?
The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions. Explain your reasoning for a, b, and c.
a. f(x) = x + 3
b. f(x) = 73 if x>2 otherwise f(x) = -1
c. f(x) = 79if x>0 or f(x) = -9 if x<0 or f(x) = 9 or -9 if x = 0
1 answer