Which relation is not a function? a) input: name of student; output: gpa b) input: price of an item; output: upc code eliminate c) input: name of student; output: birth month d) input: next door neighbors; output: zip code e) input: name of high school; output: total number of scholarships awarded

(B)

Steps:

(A) valid function because a student can only be associated with one GPA

(B) not a function: given a price there may be multiple products and therefore multiple UPC codes

(C) valid function: given a student there is only one possible month value

(D) valid function: if the neighbors are identified uniquely, and live only in one residence, then there is only one zip code for them

(E) valid function: number of scholarships awarded by a given high school is a single value for that entity.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.