Textbook Question
Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. g(x) = -2|x+3|+2
Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 3, Problem 93
Use the graphs of f and g to evaluate each composite function.
(go f) (0)
Verified step by step guidance1
Step 1: Understand the composite function (g ∘ f)(0). This means you first evaluate f(0) and then use the result as the input for g(x).
Step 2: Locate the value of f(0) on the graph of f(x) (red curve). Find the point where x = 0 and determine the corresponding y-value.
Step 3: Use the y-value obtained from f(0) as the input for g(x). Locate this value on the x-axis of the graph of g(x) (blue curve).
Step 4: Find the corresponding y-value on the graph of g(x) for the input obtained from Step 2.
Step 5: The final result of (g ∘ f)(0) is the y-value obtained from Step 4.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Composition
Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, the notation (g o f)(0) means to first evaluate f at 0, and then use that result as the input for g. Understanding this process is crucial for evaluating composite functions correctly.
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Function Composition
Evaluating Functions from Graphs
To evaluate functions from their graphs, one must identify the corresponding output values for given input values. For instance, to find f(0), locate 0 on the x-axis of the graph of f and determine the corresponding y-value. This skill is essential for accurately performing function evaluations in composite functions.
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4:26Evaluating Composed Functions
Graph Interpretation
Interpreting graphs involves analyzing the visual representation of functions to extract information about their behavior, such as intercepts, slopes, and continuity. In this exercise, understanding how to read the graphs of f and g will help in determining the values needed for the composite function evaluation.
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Guided course
02:16Graphs and Coordinates - Example
Related Practice
Textbook Question
In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
Textbook Question
Let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g(-1) and f(g(-1)).
Textbook Question
The functions in Exercises 93–95 are all one-to-one. For each function, (a) find an equation for f-1(x), the inverse function. (b) Verify that your equation is correct by showing that f(f-1(x)) = x and f-1(f(x)) = x. f(x) = 4x - 3
Textbook Question
Let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g (1) and f(g(1)).
Textbook Question
Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. h(x) = 2|x+3|