Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 93

Chapter 3, Problem 93

Use the graphs of f and g to evaluate each composite function.

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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.

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.

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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Related Practice

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

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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.

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

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Textbook Question

Let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g (1) and f(g(1)).

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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|

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Use the graphs of f and g to evaluate each composite function.(go f) (0)

Verified video answer for a similar problem:

Key Concepts

Function Composition

Evaluating Functions from Graphs

Graph Interpretation

Use the graphs of f and g to evaluate each composite function.

(go f) (0)