190 Chapter 3 Graphs, Relations, and Functions 100. Let f (x) = ux - 1u. a. Solve the equation f (x) = 2 using the methods from Section 2.6. b. Graph f (x) and draw a horizontal line through y = 2 on the same coordinate system. c. What are the points, if any, where the graph of f (x) and the horizontal line intersect? How do the points of intersection relate to the solutions of the equation? d. Solve f (x) > 2 using the methods from Section 2.7. e. On your graph from part (b), shade the portion of the x-axis that corresponds to the solution set of the inequality in part (d). f. How can the graph be used to solve the inequality? 101. Let f (x) = ux + 4u. a. Solve the equation f (x)=-1 using the methods from Section 2.6. b. Graph f (x) and draw a horizontal line through y=-1 on the same coordinate system. c. What are the points, if any, where the graph of f (x) and the horizontal line intersect? How do the points of intersection relate to the solutions of the equation? d. Solve f (x)>-1 using the methods from Section 2.7. e. On your graph from part (b), shade the portion of the x-axis that corresponds to the solution set of the inequality in part (d). f. How can the graph be used to solve the inequality? 102. Let f (x) = ux - 3u. a. Solve the equation f (x)=-2 using the methods from Section 2.6. b. Graph f (x) and draw a horizontal line through y=-2 on the same coordinate system. c. What are the points, if any, where the graph of f (x) and the horizontal line intersect? How do the points of intersection relate to the solutions of the equation? d. Solve f (x)<-2 using the methods from Section 2.7. e. On your graph from part (b), shade the portion of the x-axis that corresponds to the solution set of the inequality in part (d). f. How can the graph be used to solve the inequality? SECTION 3.4 The Domain and Range of Functions ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Find the domain and range of a function given a set, a mapping, or a table. 2. Find the domain and range of a function given a graph. 3. Find the domain of a function given an equation. 4. Apply the concept of domain to real-world situations. 5. Troubleshoot common errors. Many websites require us to enter a login name and a password to access their site. The correspondence of a login name and password form a function since each login name can have only one password. Have you ever entered your login name incorrectly and received the message that your login name is invalid? This is because the incorrect login name is not in the domain of this function. In this section, we will define and determine the domain and range of a function. Domain and Range of a Function In Section 3.2, we learned how to find the domain and range of a relation. Because every function is a relation, the steps for finding the domain and range of a function are the same. Procedure: Finding the Domain and Range of a Function Step 1: The domain is the set of x-values in the given set of points. Step 2: The range is the set of y-values in the given set of points. Objective 1 Examples Find the domain and range of each function. 1a. {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)} 1b. The table shows the five most populated states along with the party of their Governor in 2011. (Source: en.wikipedia.org) State California Texas New York Florida Illinois Party Democrat Republican Democrat Republican Democrat Objective 1 ▶ Find the domain and range of a function given a set, a mapping, or a table.
hendricks_intermediate_algebra_1e_ch1_3
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