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
2. Graphs of Equations
Two-Variable Equations
3:10 minutes
Problem 23b
Textbook Question
Textbook QuestionGraph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = |x| + 1
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value Function
The absolute value function, denoted as |x|, measures the distance of a number x from zero on the number line, always yielding a non-negative result. For example, |3| = 3 and |-3| = 3. This function is crucial for understanding how the graph behaves, as it creates a V-shape that opens upwards.
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Graphing Linear Equations
Graphing linear equations involves plotting points on a coordinate plane that satisfy the equation. In this case, the equation y = |x| + 1 combines the absolute value function with a vertical shift upwards by 1 unit. Understanding how to plot points and interpret the resulting shape is essential for visualizing the function.
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Domain and Range
The domain of a function refers to all possible input values (x-values), while the range refers to all possible output values (y-values). For the equation y = |x| + 1, the domain includes all real numbers, and the range starts from 1 and goes to infinity, as the minimum value occurs when x = 0. Recognizing these concepts helps in accurately sketching the graph.
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