Download ArticleEasy homework help for functions in algebra or precalculus
Download ArticleThis article was written by Joseph Meyer and by How.com.vn staff writer, Kyle Smith. Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.
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Do you need to determine whether a relation is a function? The process may sound difficult, but it's actually pretty easy. To know if a relation is a function, just examine the inputs and outputs. When you’re given a set of ordered pairs, check whether any inputs have multiple outputs. If so, the relation is not a function. You can also do the vertical line test to check whether a relation is a function. This How.com.vn guide shows you how to know when a relation is a function.
Things You Should Know
- Relations are a set of inputs and outputs, often shown as ordered pairs or a table.
- Functions are relations in which each input has exactly one output.
- Check whether each input has one output to know if a relation is a function.
Steps
Definitions
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Relations are a set of inputs and outputs. The inputs (domain) are paired with outputs (range).
Functions occur when each input has exactly one output. Different inputs can have the same output value. An input can not be assigned to multiple output values.- If you’re looking for quadratic function information, check out our guides on finding the inverse and finding the max or min.
Evaluate the Relation
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Put your ordered pairs into a table. If you were given a set of ordered pairs, putting them into a table is helpful for checking if the relation is a function. Skip this step if you already have a table of inputs and outputs.- Take the left value (the x value) of each ordered pair and place them vertically in the left column (input) of a 2 column table.
- Repeat for the right values (the y values), placing them in the right column (output).
Check whether any inputs have multiple outputs. If an input has multiple outputs, the relation is not a function.
Take a look at this non-function example. You’re given the following set of ordered pairs. Because the input 1 has two outputs, 2 and 7, this relation is not a function.- (1, 2)
- (2, 4)
- (3, 10)
- (1, 7)
- (5, 0)
Check out this function example. You’re given the following set of ordered pairs. Because each input only has one output, this relation is a function. Functions can have different inputs assigned to the same output. In this case, the inputs 3 and 4 have both been assigned to 10.- (1, 2)
- (2, 4)
- (3, 10)
- (4, 10)
- (5, 0)
Vertical Line Test
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Plot the ordered pairs on a graph. Place a dot at each given ordered pair coordinate on an XY plane.
Move a vertical line across the graph. Use a straight-edge (like a ruler or another sheet of paper) to move a vertical line (parallel to the Y axis) across the entire graph. If the vertical line hits two or more points at the same X location, the relation is not a function.- In other words, if two or more points have the same X value and different Y values, the relation is not a function.
- The relation is a function if you move the vertical line across the graph without hitting two or more points at the same time.
Expert Q&A
Tips
- For general math tips, check out our guide on how to learn math.Thanks
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