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". When we have a function, no vertical line will intersect the graph in more than one location.

Test Objectives
• Demonstrate an understanding of the concept of a function
• Demonstrate an understanding of domain and range
• Demonstrate the ability to use the vertical line test to determine if a relation represents a function
Functions Vertical Line Test Practice Test:

#1:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}y=-\frac{1}{2}x + 2$$

#2:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}|y|=x + 2$$

#3:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}y=(x - 6)^2 + 1$$

#4:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}y=x^3 - x$$

#5:

Instructions: determine if each relation is a function.

$$a)\hspace{.2em}(x + 2)^2 + y^2=36$$

Written Solutions:

#1:

Solutions:

a) Function

#2:

Solutions:

a) Not a Function

#3:

Solutions:

a) Function

#4:

Solutions:

a) Function

#5:

Solutions:

a) Not a Function