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hendricks_intermediate_algebra_1e_ch1_3

Plot the points. Note that the points lie in a V-shaped pattern. Connect the points to form the V-shape. Arrows are used to indicate the graph continues indefinitely in each direction. The V-shaped graph represents the solution set of y = |x + 1|. Student Check 3 Graph each equation by plotting points. a. y = x + 3 b. y = x2 + 1 c. y = |x| Using a Graph to Determine Solutions In Objective 2, we determined if an ordered pair was a solution of an equation by substituting the values of x and y in the equation and determining if the resulting equation was true or false. We can also determine if an ordered pair is a solution of an equation by examining its graph. Procedure: Determining Graphically if an Ordered Pair Is a Solution of an Equation Step 1: Graph the equation, if needed. Step 2: Plot the point. a. If the point lies on a graph, then it is a solution of the graphed equation. b. If the point does not lie on a graph, then it is not a solution of the graphed equation. Objective 4 ▶ Determine graphically if an ordered pair is a solution of an equation. Objective 4 Examples The graph of y = x2 - 4 is provided. Use the graph to determine if the given ordered pair is a solution of y = x2 - 4. 4a. (-4, 0) 4b. (0, -4) 4c. (2, 0) 4d. (0, 2) 4e. (-3, 5) Solution The points (0, -4), (2, 0), and (-3, 5) lie on the graph. So, these points are solutions of the equation. The points (-4, 0) and (0, 2) do not lie on the graph. So, these points are not solutions of the equation. 2 2 4 4 –2 –4 –2 –4 x y 2 2 4 4 –2 (–3 5) –4 –2 –4 x y (–4 0) (2 0) (0 2) (0 –4) 2 2 4 4 –2 –6 –4 –2 –4 x y 2 2 4 4 –2 –6 –4 –2 –4 x y 154 Chapter 3 Graphs, Relations, and Functions


hendricks_intermediate_algebra_1e_ch1_3
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