Domanda del libro di testo
Use the graphs of f and g to solve Exercises 83–90.
Find (fg) (2).
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 3, Problema 84a
Use the graphs of f and g to solve Exercises 83–90.
Find (g-f) (-2).
Guida verificata passo dopo passo1
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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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.
Video consigliato:
4:26
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.
Video consigliato:
4:56Function Composition
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).
Video consigliato:
02:16Graphs and Coordinates - Example
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