Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
3. Functions
Intro to Functions & Their Graphs
2:58 minutes
Problem 21e
Textbook Question
Textbook QuestionFor each graph, determine whether y is a function of x. Give the domain and range of each relation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Definition
A function is a relation where each input (x-value) corresponds to exactly one output (y-value). To determine if y is a function of x, one can use the vertical line test: if a vertical line intersects the graph at more than one point, then y is not a function of x.
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Domain and Range
The domain of a function is the set of all possible input values (x-values) that can be used without causing any mathematical issues, such as division by zero. The range is the set of all possible output values (y-values) that result from the domain. Identifying these sets is crucial for understanding the behavior of the function.
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Graph Interpretation
Interpreting graphs involves analyzing the visual representation of a function or relation to extract information about its characteristics, such as intercepts, symmetry, and overall shape. In this case, recognizing the parabolic curves and their intersections with the y-axis helps in determining the function's properties and the domain and range.
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