Calculus I: Functions and their graphs · Functions, Domain and Range
What makes a rule a function, how to find its domain and range, and when it has an inverse.
Calculus I · 28 questions
Try 3 questions
1. What makes a rule that pairs inputs with outputs a function?
- Every input and output is a number
- Each input has exactly one output
- Each output comes from exactly one input
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Answer: Each input has exactly one output
A function may send many inputs to the same output, but it can never send one input to two different outputs.
2. Why does the circle x² + y² = 1 not define y as a function of x?
- Most x-values pair with two y-values
- It never passes through the origin
- Its graph has no straight segments
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Answer: Most x-values pair with two y-values
For x = 0, both y = 1 and y = −1 lie on the circle, so one input has two outputs.
3. A curve passes the vertical line test. What does that guarantee?
- It is the graph of a function of x
- The function has an inverse
- The function is continuous
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Answer: It is the graph of a function of x
A vertical line hitting the curve twice would mean one x with two y-values; never doing so is exactly the definition of a function.
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