Sure! Here’s how you can structure your Math Practice for Unit 6, Lesson 1 about functions, along with responses to the questions and space for illustrations as needed.
What do you know?
- A function is a relationship where each input has one and only one output.
- An input is the value you put into a function.
- An output is the result you get from a function after applying the input.
- Functions can be represented in different forms: graphs, tables, and equations.
- A vertical line test can be used to determine if a graph represents a function.
- If a table of values has two inputs (x-values) that are the same but different outputs (y-values), it is not a function.
- An equation represents a functional relationship if each input corresponds to exactly one output.
Vocabulary Terms - Define/Illustrate
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Input: The value or values you provide to a function.
- Illustration: Example: For the function f(x) = x + 2, if x = 3, then input is 3.
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Output: The value you get after applying the function to the input.
- Illustration: Using the same function, if the input is 3, then output is 5 (f(3) = 3 + 2).
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Function: A specific kind of relation where each input has exactly one output.
- Illustration: Graphing f(x) = x^2 shows that each x-value has only one corresponding y-value.
5 Problems - SHOW ALL WORK!
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How can we determine from a graph if a function is shown or not?
- You can use the vertical line test: if a vertical line crosses the graph more than once, it is not a function.
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How can you tell from a table of values if the relationship is a function or not?
- Look for duplicate x-values (inputs). If any x-value has more than one corresponding y-value (output), it is not a function.
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How can you tell from an equation if the relationship is a function?
- If for every x-value there is only one possible y-value when the equation is solved, then it is a function.
Application Questions
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Is the number of students on a field trip a function of the number of buses used? Explain.
- Yes, it can be considered a function because for each number of buses used, there can be a specific and determined number of students that can fit on those buses.
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Is the time it takes you to run a 100-meter race a function of the speed you run? Explain.
- Yes, it is a function because if you know the speed, you can determine the time it takes to run the race (time = distance / speed).
What do I need help with?
(Leave this section blank for you to fill in specific areas where you may have questions or need clarification on the concepts discussed.)
Feel free to add any additional work or drawings as needed, and make sure to reach out with questions where needed for further help!