Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problema 85

Capitolo 3, Problema 85

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

Find (fg) (2).

Guida verificata passo dopo passo

Step 1: Understand the problem. You are tasked with finding (fg)(2), which means you need to evaluate the product of the functions f(x) and g(x) at x = 2.

Step 2: Locate x = 2 on the graph. Look at the horizontal axis and find the point where x = 2.

Step 3: Determine the value of f(2). Find the red graph (representing f(x)) and identify the y-coordinate of the point where x = 2.

Step 4: Determine the value of g(2). Find the blue graph (representing g(x)) and identify the y-coordinate of the point where x = 2.

Step 5: Multiply the values of f(2) and g(2). Once you have the values of f(2) and g(2), multiply them together to find (fg)(2).

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Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, if we have a function f(x), evaluating it at x = 2 means finding f(2). This is essential for solving problems that require specific outputs from given functions.

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Evaluating Composed Functions

Product of Functions

The product of two functions, denoted as (fg)(x), is defined as the multiplication of their outputs at a given input x. Specifically, (fg)(x) = f(x) * g(x). To find (fg)(2), one must first evaluate f(2) and g(2), then multiply these results together.

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Special Products - Cube Formulas

Graph Interpretation

Interpreting graphs of functions involves analyzing the visual representation of the functions to extract information such as values at specific points. In this case, the graphs of f(x) and g(x) can be used to find f(2) and g(2) by locating the corresponding y-values at x = 2 on their respective graphs.

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Graphs and Coordinates - Example

Pratica correlata

Domanda del libro di testo

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.

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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

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

Find(g/f)(3)

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Domanda del libro di testo