A relation is any set of ordered pairs (x,y). A function is a special type of relation where there is a one to one correspondence. Each first component or x value corresponds to or is linked to exactly one second component or y value. Many times we hear this read as ‘for each x, there can be only one y’.
Test Objectives:•Understand the definition of a relation
•Understand the difference between domain and range
•Demonstrate the ability to determine if a relation represents a function
Introduction to Functions Test:
#1:
Instructions: Determine if each relation is a function, then list the domain and range.
a) {(3,2), (1,-7), (8,-6), (2,3), (0,5)}
#2:
Instructions: Determine if each relation is a function, then list the domain and range.
a) {(6,3), (1,7), (6,-2)}
#3:
Instructions: Determine if each relation is a function, then list the domain and range.
a) {(-1,0), (-2,3), (7,-8), (1,0)}
#4:
Instructions: Determine if each relation is a function, then list the domain and range.
a) {(-20,5), (32, 10), (-20,7), (8,6)}
#5:
Instructions: Determine if each relation is a function, then list the domain and range.
a) {(-3,5), (7,-1), (0,15), (6,2)}
Written Solutions:
Solution:
a) Yes - this relation is a function
domain = {3,1,8,2,0}
range = {2,-7,-6,3,5}
Solution:
a) No - this relation is not a function
domain = {6,1}
range = {3,7,-2}
Solution:
a) Yes - this relation is a function
domain = {-1,-2,7,1}
range = {0,3,-8}
Solution:
a) No - this relation is not a function
domain = {-20,32,8}
range = {5,10,7,6}
Solution:
a) Yes - this relation is a function
domain = {-3,7,0,6}
range = {5,-1,15,2}