Identifying Functions &
Using the Vertical Line Test
Now that you've studied the three examples from our first functions lesson are you ready to try a few on your own?
Let's recap a few things that will help you identify whether the following relations are functions.
A relation is only a function if each input is only paired with one output. In other words - focus on your x coordinate (input). If you have 2 or more x coordinates that are the same - they must all have the same output or it is not a function!
If you are using the vertical line test, and your "line" touches the graph in more than one point, then it is not a function! Your vertical line must only touch the graph at one point!
Ok... let's try a few practice problems!
Practice Problems
Directions: Using the vertical line test, determine if the relation is a function.
1.
2.
Directions: For the next two problems, determine whether the relations, written as ordered pairs, are functions. You can use the vertical line test if you choose to graph the ordered pairs.
Click here to print out graph paper.
1. {(-5, -1) (3,3) (1, 2) (-5, 7) }
2. {(-3, 1) (-1, -1) (3,0) (-2, -4)}
Ready to check your answers?
Answer Key
1. Yes, this graph represents a function. The vertical lines only pass through one point on the graph.
2. Yes, this graph represents a function. The vertical lines only pass through one point on the graph.
3. NO, this relation is NOT a function. The -5 is paired up with two different outputs.
4. YES, this relation is a function. Each input is paired up with a different output!
Great Job! Next we will focus on function notation and evaluating functions!
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