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
• Understand the definition of a relation
• Understand the difference between domain and range
• Demonstrate the ability to use the vertical line test to determine if a relation represents a function
Vertical Line Test Practice Test:

#1:

Instructions: Determine if each relation is a function using the vertical line test, then list the domain and range.

a) $$y = -4x + 2$$ #2:

Instructions: Determine if each relation is a function using the vertical line test, then list the domain and range.

a) $$y = x^2 + 7$$ #3:

Instructions: Determine if each relation is a function using the vertical line test, then list the domain and range.

a) $$y = \frac{5}{x^2 - 1}$$ #4:

Instructions: Determine if each relation is a function using the vertical line test, then list the domain and range.

a) $$y^2+x^2=16$$ #5:

Instructions: Determine if each relation is a function using the vertical line test, then list the domain and range.

a) $$x = -3(y - 1)^2 - 1$$ Written Solutions:

#1:

Solutions:

a) Yes - this relation is a function

$$domain = \left\{x|x ∈ ℝ\right\}$$ $$range = \left\{y|y ∈ ℝ\right\}$$

#2:

Solutions:

a) Yes - this relation is a function

$$domain = \left\{x|x ∈ ℝ\right\}$$ $$range = \left\{y|y ≥ 7\right\}$$

#3:

Solutions:

a) Yes - this relation is a function

$$domain = \left\{x|x ≠-1,1\right\}$$ $$range = \left\{y|y ≤-5~or~y > 0\right\}$$

#4:

Solutions:

a) No - this relation is not a function

$$domain = \left\{x|-4 ≤ x ≤ 4\right\}$$ $$range = \left\{y|-4 ≤ y ≤ 4\right\}$$

#5:

Solutions:

a) No - this relation is not a function

$$domain = \left\{x|x ≤ -1\right\}$$ $$range = \left\{y|y ∈ ℝ\right\}$$