Ch. 2 - Functions and Graphs

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

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 83a

Chapter 3, Problem 83a

Use the graphs of f and g to solve Exercises 83–90.

Find (f+g)(−3).

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Step 1: Understand the problem. You are tasked with finding (f+g)(−3), which means you need to evaluate f(−3) and g(−3) from the graph and then add the two values together.

Step 2: Locate x = −3 on the graph. Look at the blue graph labeled y = f(x) and the red graph labeled y = g(x) to find the corresponding y-values for x = −3.

Step 3: Determine f(−3). Find the point on the blue graph where x = −3 and note the y-coordinate of that point. This is the value of f(−3).

Step 4: Determine g(−3). Find the point on the red graph where x = −3 and note the y-coordinate of that point. This is the value of g(−3).

Step 5: Add the values. Once you have f(−3) and g(−3), add them together to find (f+g)(−3).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Addition

Function addition involves combining two functions, f(x) and g(x), to create a new function (f + g)(x) defined as (f + g)(x) = f(x) + g(x). This operation requires evaluating both functions at a given input and summing their outputs. Understanding how to read and interpret function values from graphs is essential for performing this operation.

Evaluating Functions from Graphs

To evaluate functions from their graphs, one must locate the x-value on the horizontal axis and determine the corresponding y-value on the vertical axis for each function. For the question, finding (f + g)(−3) requires first identifying f(−3) and g(−3) from their respective graphs, then adding these values together to find the result.

Graph Interpretation

Graph interpretation is the ability to analyze and extract information from visual representations of functions. This includes recognizing key features such as intercepts, slopes, and the overall shape of the graph. In this context, understanding how to read the graphs of f(x) and g(x) is crucial for accurately determining their values at specific points, such as x = -3.

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Related Practice

Textbook Question

Find f + g, f - g, fg, and f/g. f(x) = x² + x + 1, g(x) = x² -1

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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.

Textbook Question

In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x) = 3x - 1, g(x) = x - 5

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) = |x|+3

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) = |x+3|

Textbook Question

In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x) = √(x + 7), g(x) = √(x - 2)

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Use the graphs of f and g to solve Exercises 83–90.Find (f+g)(−3).

Verified video answer for a similar problem:

Key Concepts

Function Addition

Evaluating Functions from Graphs

Graph Interpretation

Use the graphs of f and g to solve Exercises 83–90.

Find (f+g)(−3).