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 92

Capitolo 3, Problema 92

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.

Guida verificata passo dopo passo

Step 1: Identify the domain of the function by looking at the x-values for which the function has points plotted. From the graph, the points are plotted at x = -5, -4, -3, -2, -1, 1, 2, 3, and 4. So, the domain is the set of these x-values.

Step 2: Determine the range of the function by noting the y-values of the plotted points. From the graph, all points lie on the line y = -2, so the range is just the single value y = -2.

Step 3: Find the x-intercepts by checking where the graph crosses the x-axis (where y = 0). Since all points have y = -2, the graph does not cross the x-axis, so there are no x-intercepts.

Step 4: Find the y-intercept by checking the value of the function at x = 0. Since there is no point plotted at x = 0, the function has no y-intercept.

Step 5: To find the value of f(-5) + f(4), read the y-values of the points at x = -5 and x = 4 from the graph. Both points have y = -2, so add these two values together to get the sum.

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Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In a graph, the domain corresponds to the horizontal extent of the plotted points or curve. Identifying the domain helps determine which x-values can be used to find corresponding y-values.

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Domain Restrictions of Composed Functions

Range of a Function

The range of a function is the set of all possible output values (y-values) that the function can produce. On a graph, the range is the vertical spread of the points or curve. Understanding the range helps in knowing the limits of the function's output values.

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Function Values and Intercepts

Function values are the y-values corresponding to specific x-values, denoted as f(x). The x-intercepts are points where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0). These points are crucial for analyzing the behavior and key features of the function.

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Graphing Intercepts

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