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Functions

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1. Explain what is meant by a function. Give two real-world examples of relationships that are functions and two real-world examples that are not functions.
2. How many x-intercepts can a function have? Give a specific example and state the rule that backs up your answer.
3. Explain how the vertical line test works to prove if a graph is a function or not. Research and explain what the horizontal line test is used to prove for functions.
4. A classmate tells you that every quadratic function of the form f(x) = ax2 + bx + c has a domain of all real numbers. Do you agree? Explain.
5. Suppose that f is a function. Given, f(a) = f(b). Does this imply a = b? Prove with a specific example.

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Solution Summary

This provides examples and explanations regarding functions: definitions, intercepts, and domain.

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Explain what is meant by a function. How many x-intercepts can a function have?

1. Explain what is meant by a function. Give two real-world examples of relationships that are functions and two real-world examples that are not functions.
Solution:

Solution:

In mathematics, a function is a relation in which for each value of x there is one and only ONE y-value.

Two real-world examples of relationships that are functions:

1. Earning depends on hours worked
2. Volume of sphere depends on radius

Two real-world ...

Solution provided by:
Sandhya Sharma, MSc
Education
  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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