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In Exercises 59–94, solve each absolute value inequality. - 2|x - 4| ≥ - 4
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Ch. 1 - Equations and Inequalities
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 2, Problema 80
In Exercises 77–92, use the graph to determine a. the function's domain; b.the x-intercepts, if any; and e. the missing function values, indicated by question marks, below each graph. 
Guida verificata passo dopo passo1
Step 1: To determine the domain of the function, observe the x-values for which the function is defined. For the first graph, the function is defined from x = 0 to x = 4. For the second graph, the function is defined for all x-values.
Step 2: To find the x-intercepts, look for the points where the graph crosses the x-axis. For the first graph, the x-intercept is at (4, 0). For the second graph, the x-intercept is at (0, 0).
Step 3: To find the missing function values, locate the corresponding y-values for the given x-values on the graph. For the second graph, find the y-values for x = -4 and x = 3.
Step 4: For the second graph, when x = -4, trace vertically to the graph to find the y-value. Similarly, when x = 3, trace vertically to the graph to find the y-value.
Step 5: Summarize the findings: The domain, x-intercepts, and missing function values for each graph.
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Domain of a Function
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. Understanding the domain is crucial for determining where the function can be evaluated, which can be influenced by factors such as discontinuities or restrictions in the function's definition.
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Domain Restrictions of Composed Functions
X-Intercepts
X-intercepts are the points where a function crosses the x-axis, meaning the output value (y) is zero at these points. To find x-intercepts, one typically sets the function equal to zero and solves for x. Identifying these points is essential for understanding the behavior of the function and its graphical representation.
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04:08Graphing Intercepts
Function Values
Function values represent the output of a function for given input values. In the context of a graph, these values can be determined by evaluating the function at specific x-values. Missing function values, often indicated by question marks, require careful analysis of the graph to estimate or calculate the corresponding y-values.
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4:56Function Composition
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