Procedure: Finding the Domain of a Function from Its Graph Step 1: Determine the x-value of the leftmost point on the graph. Step 2: Determine the x-value of the rightmost point on the graph. Step 3: The domain is the interval between the x-values of the points found in steps 1 and 2. Note: If the graph extends indefinitely from the left to the right, the domain is all real numbers, denoted by (-∞,∞). Procedure: Finding the Range of a Function from Its Graph Step 1: Determine the y-value of the lowest point on the graph. Step 2: Determine the y-value of the highest point on the graph. Step 3: The range is the interval between the y-values of the points found in steps 1 and 2 Note: If the graph extends indefinitely from the bottom to the top, the range is all real numbers, denoted by (-∞, ∞). Objective 2 Examples Find the domain and range of each function. 2a. 2b. 2c. 6 2 –4 –2 2 x 4 4 –2 y 6 2 –2 2 x 4 4 6 –2 y 2 2 4 4 –2 –4 –2 –4 x y Solutions 2a. The graph extends indefinitely to the left and right, so the domain is (-∞, ∞). The lowest and highest points on the graph are both on the line y = 4 since every point on the line has a y-value of 4. So, the range is {4}. (See Figure 3.4.1.) 2b. The graph extends indefinitely to the left and right, so the domain is (-∞, ∞). The lowest point on the graph is (2, 0). The graph doesn’t have a highest point since it extends indefinitely upward. So, the range is 0, ∞). (See Figure 3.4.2.) 2c. The graph extends indefinitely to the left. The rightmost point is (2, -1). So, the domain is (-∞, 2. The lowest point on the graph is (2, -1). The graph extends indefinitely upward. So, the range is -1, ∞). (See Figure 3.4.3.) 6 2 y y 2 4 4 –2 6 4 2 0 –2 –4 –2 x –4 –2 0 2 4 x 6 2 y y 2 4 4 6 –2 6 4 2 0 –2 –2 x –2 0 2 4 6 x 2 2 4 y 4 4 –4 –2 –4 x –4 –2 0 2 4 x 0 –2 y 2 –2 –4 Between what values of x is the graph contained? Between what values of y is the graph contained? Figure 3.4.2 Figure 3.4.1 Figure 3.4.3 192 Chapter 3 Graphs, Relations, and Functions
hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above