U03_L2_T1_we2 Representing Functions as Graphs | Summary and Q&A
TL;DR
The points on the graph do not represent a function because one x-value is mapped to two different y-values.
Key Insights
- βΊοΈ A function maps an input value to an output value, usually denoted as x and y.
- π A function should have a unique output value for each input value or be undefined for certain inputs.
- β£οΈ The points on the given graph do not represent a function because an x-value of 4 is mapped to two different y-values.
- β£οΈ Having multiple y-values for the same x-value violates the requirement for a function.
- π₯ The points on a graph can be used to determine if they represent a function by checking for unique mappings or undefined values.
- π In the given graph, the point (6, ?) is undefined because the function is not defined for the x-value of 6.
- β£οΈ When analyzing a graph to determine if it represents a function, each x-value must correspond to only one y-value.
Transcript
We're asked: Do the points on the graph below represent a function? Now, before even attempting to do this problem, let's just remind ourselves what they mean by a function. A function literally just takes some input, and it's usually considered x, some number x, but it takes some input. Let me do it in a darker color. So it takes some input, let's... Read More
Questions & Answers
Q: How is a function defined?
A function takes an input (usually x) and maps it to an output value. It should either produce a unique y-value for every x-value or be undefined for certain x-values.
Q: Can a function map one x-value to multiple y-values?
No, a function should map each x-value to only one y-value. Having multiple y-values for the same x-value violates the definition of a function.
Q: Why is the point (6, ?) undefined in the given graph?
The point (6, ?) is undefined because the function has not been defined or specified for the x-value of 6.
Q: Why do the points on the graph not represent a function?
The points on the graph do not represent a function because an x-value of 4 is mapped to both -1 and 5, violating the requirement for a function to have a unique output value for each input value.
Summary & Key Takeaways
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A function takes an input (usually denoted as x) and maps it to an output value, which is typically represented as f(x) or y.
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For the points on the given graph to represent a function, there should be a unique y-value for every x-value, or the function should be undefined for certain x-values.
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In the given graph, an x-value of 4 is mapped to both -1 and 5, violating the requirement for a function.