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 90a

Capitolo 3, Problema 90a

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

Graph f-g.

Guida verificata passo dopo passo

Step 1: Understand the problem. You are tasked with graphing the function f(x) - g(x), which represents the difference between the y-values of f(x) (blue graph) and g(x) (orange graph) at each x-coordinate.

Step 2: Identify key x-values where both f(x) and g(x) are defined. These include x = -6, -4, -2, 0, 2, 4, 6, and 8. For each x-value, note the corresponding y-values of f(x) and g(x).

Step 3: Calculate f(x) - g(x) for each x-value. Subtract the y-value of g(x) from the y-value of f(x) at each x-coordinate. For example, at x = -6, f(x) = 6 and g(x) = -6, so f(x) - g(x) = 6 - (-6) = 12.

Step 4: Plot the points (x, f(x) - g(x)) on the graph. For example, at x = -6, the point would be (-6, 12). Repeat this for all x-values.

Step 5: Connect the plotted points to form the graph of f(x) - g(x). Ensure the graph reflects the calculated differences and follows the general shape dictated by the subtraction of the two functions.

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Function Subtraction

Function subtraction involves taking two functions, f(x) and g(x), and creating a new function h(x) = f(x) - g(x). This new function represents the vertical distance between the graphs of f and g at any given x-value. Understanding how to perform this operation is essential for graphing the resulting function.

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Adding & Subtracting Functions

Graphing Functions

Graphing functions requires plotting points on a coordinate plane based on the function's output values for given input values. For the functions f(x) and g(x), one must accurately represent their values on the graph to visualize their behavior. This skill is crucial for understanding how to combine functions through operations like subtraction.

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Graphs of Logarithmic Functions

Vertical Shifts

When subtracting one function from another, the resulting graph can be interpreted as a vertical shift of the original functions. The graph of h(x) = f(x) - g(x) will show where f(x) is above or below g(x), indicating the points of intersection and the overall relationship between the two functions. Recognizing these shifts helps in accurately sketching the graph of the resulting function.

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Shifts of Functions

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