Question

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

Answer 1

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?