Lesson 1 of 6
Tell inputs from outputs and evaluate a rule with care.
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Big ideas · 1 of 9
Big ideas
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A FunctionA rule that gives one output for each allowed input.Exactly: A function assigns exactly one value in its codomain to each element of its domain.Mix-up alert: Different inputs can have the same output.See this in Key words gives exactly one output for each allowed input. Different inputs may share an output.
In , the input is 3 and the output is 7. The parentheses name an input; they do not mean multiplication.
Replace each x with the complete input, using parentheses for negative numbers or expressions. Work through the operations in order.
Words, ordered pairs, a table and a rule can describe the same function. Label quantities and units before interpreting a result.
Step-through
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Worked example: evaluate a negative input
Whole picture, 4 steps
4 steps. Tap a number or Show me how it works.
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Answer: .
Do this: Cover the next step and try it yourself.
The input is a count; the output is a cost.
Do this: Explain why the tempting shortcut fails.
Wrong idea: means f times −3. Instead, f names a rule and −3 is the input. For , write ; the negative sign belongs inside the substitution parentheses.
Worked example
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Worked example
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Tip
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Class handout reference · Unit 2, sections 2.1 and 2.2. Use your class copy.
Watch
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Ready when you are.
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Flashcards
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Card 1 of 8
0 Know it0 Still learning
Check repeated inputs, not repeated outputs.
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What makes a relation a function?
Every allowed input has exactly one output.
In , which number is the input?
8 is the input; 13 is the output.
Can two inputs share the same output?
Yes. For example, sends both −2 and 2 to 4.
For , find .
because .
For , find .
because .
What does a point on mean?
: input 2 produces output 9.
How does a vertical line test work?
If a vertical line hits a graph more than once, one input has multiple outputs.
Why label units in a function model?
They identify the input quantity and the output quantity so a value has meaning.
True or false
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Self-test
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6 questions. One at a time.
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Self-test
Do this: Try each problem without a timer. Read the feedback before moving on.
6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Write it
Do this: Write two or three sentences, then compare with the model.
Start here if it helps: I would first identify...
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Write it
Do this: Write a mathematical argument, then compare its reasoning with the model.
Start here if it helps: My argument starts with...
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Match
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Connect the ideas
0 / 4 connectedChoose a term, then its meaning. Or drag its grip. Use Tab and Enter or Space; Escape clears.
Homework · 3 points
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Homework
Worth 3 points.
https://gradebridge-beryl.vercel.app/learn/precalculus/functions/function-notation#homework
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