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
Problem 78c
Textbook Question
Textbook QuestionIn Exercises 77–92, use the graph to determine a.the x-intercepts, if any; b. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph. ![Graph showing x-intercepts at (0,0) and (5,0), y-intercept at (0,7).](https://lightcat-files.s3.amazonaws.com/problem_images/6e6ff08e1ae973b2-1673540482966.jpg)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
X-Intercepts
X-intercepts are the points where a graph crosses the x-axis, indicating where the function's output (y-value) is zero. To find x-intercepts, set the function equal to zero and solve for x. In the provided graph, the x-intercepts are at the points (0,0) and (5,0).
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Y-Intercepts
The y-intercept is the point where a graph crosses the y-axis, representing the value of the function when x is zero. To determine the y-intercept, evaluate the function at x = 0. In the graph, the y-intercept is at the point (0,7), indicating that the function's value is 7 when x is zero.
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Function Values
Function values refer to the outputs of a function for given inputs. In the context of the graph, missing function values can be identified by observing the graph at specific x-values. These values can be estimated visually or calculated if the function's equation is known, helping to complete the analysis of the graph.
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