Textbook Question
Use the graphs of f and g to solve Exercises 83–90.
Find (fg) (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 84a
Use the graphs of f and g to solve Exercises 83–90.
Find (g-f) (-2).
Verified step by step guidance1
Step 1: Understand the problem. You are tasked with finding the value of (g - f)(-2), which means you need to subtract the value of f(-2) from g(-2).
Step 2: Locate the x-coordinate of -2 on the graph. Look at the vertical line corresponding to x = -2 and identify the points where the functions f(x) (blue curve) and g(x) (red curve) intersect this line.
Step 3: Determine the value of f(-2). Find the y-coordinate of the blue curve at x = -2. This is the value of f(-2).
Step 4: Determine the value of g(-2). Find the y-coordinate of the red curve at x = -2. This is the value of g(-2).
Step 5: Subtract f(-2) from g(-2). Use the formula (g - f)(-2) = g(-2) - f(-2) to compute the result.
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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. In this case, we need to evaluate both functions f and g at x = -2 to find their respective values. This is a fundamental skill in algebra, as it allows us to analyze the behavior of functions at specific points.
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Evaluating Composed Functions
Difference of Functions
The difference of two functions, denoted as (g - f)(x), is calculated by subtracting the output of function f from the output of function g for the same input x. This operation helps in understanding how the two functions compare at any given point, which is essential for solving the problem at hand.
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Graph Interpretation
Interpreting graphs involves analyzing the visual representation of functions to extract information about their values, trends, and intersections. In this exercise, we will use the graph to find the values of f(-2) and g(-2) directly from the plotted points, which is crucial for accurately calculating (g - f)(-2).
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02:16Graphs and Coordinates - Example
Related Practice
Textbook Question
If one point on a line is (2, −6) and the line's slope is -3/2, find the y-intercept.
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
Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. h(x) = |x + 3| - 2
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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