U03_L2_T1_we2 Representing Functions as Graphs

TL;DR

The points on the graph do not represent a function because one x-value is mapped to two different y-values.

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

Key Insights

• ☺️ A function maps an input value to an output value, usually denoted as x and y.
• 🔠 A function should have a unique output value for each input value or be undefined for certain inputs.
• ❣️ The points on the given graph do not represent a function because an x-value of 4 is mapped to two different y-values.
• ❣️ Having multiple y-values for the same x-value violates the requirement for a function.
• 😥 The points on a graph can be used to determine if they represent a function by checking for unique mappings or undefined values.
• 👈 In the given graph, the point (6, ?) is undefined because the function is not defined for the x-value of 6.
• ❣️ When analyzing a graph to determine if it represents a function, each x-value must correspond to only one y-value.

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

• 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.

• 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.

• In the given graph, an x-value of 4 is mapped to both -1 and 5, violating the requirement for a function.