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
Function Operations
Problem 34Lial - 13th Edition
Textbook Question
Use the graph to evaluate each expression. See Example 3(a). (ƒ-g)(-1) 
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1
Identify the functions and from the graph. is the red parabola and is the blue line.
Locate the point on the x-axis and find the corresponding y-values for both and .
Read the y-value of at from the graph.
Read the y-value of at from the graph.
Subtract the y-value of from the y-value of to evaluate .
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Evaluation
Function evaluation involves substituting a specific input value into a function to determine its output. For example, if f(x) is a function, evaluating f(-1) means finding the value of the function when x equals -1. This is crucial for understanding how to compute values from the graph of the functions f(x) and g(x).
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Graph Interpretation
Graph interpretation is the ability to read and analyze graphical representations of functions. In this context, it involves identifying the values of f(-1) and g(-1) from the graph, which are necessary for calculating (f-g)(-1). Understanding how to extract information from the graph is essential for solving the problem.
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Graphs and Coordinates - Example
Function Subtraction
Function subtraction refers to the operation of subtracting the output of one function from another. In this case, (f-g)(x) means taking the value of f(x) and subtracting g(x) from it. To evaluate (f-g)(-1), one must first find f(-1) and g(-1) and then perform the subtraction, which is a fundamental operation in algebra.
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Related Practice
Textbook Question
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2
(ƒ+g)(2)
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