Section 3.2 Relations 169 To find the domain, observe that there is no leftmost point or rightmost point of the graph. The arrows indicate that the graph continues left and right indefinitely, that is, the graph extends left to -∞ and right to ∞. Since the graph continues without stopping between these values, the points on the graph have x-values between -∞ and ∞, as illustrated by Figure 3.4. So, the domain is (-∞, ∞). To find the range, observe that the graph does not have a lowest or highest point. The arrows indicate that the graph continues upward and downward indefinitely, that is, the graph extends down to -∞ and up to ∞. Since the graph continues without stopping between these values, the points on the graph have y-values between -∞ and ∞, as illustrated by Figure 3.5. So, the range is (-∞, ∞). 6 4 2 y –4 –2 2 4 6 x –2 –4 –2 0 2 4 6 x 6 –4 –2 x Procedure: Finding the Domain by Reading the Graph from Left to Right Step 1: What is the x-value of the leftmost point on the graph? Step 2: What is the x-value of the rightmost point on the graph? Step 3: Ask yourself, “Between what values of x is the graph contained?” Step 4: If the graph extends indefinitely from the left to the right, the domain is all real numbers, denoted by (-∞, ∞). 6 4 0 Procedure: Finding the Range by Reading the Graph from Bottom to Top Step 1: What is the y-value of the lowest point on the graph? Step 2: What is the y-value of the highest point on the graph? Step 3: Ask yourself, “Between what values of y is the graph contained?” Step 4: If the graph extends indefinitely from the bottom to the top, the range is all real numbers, denoted by (-∞, ∞). Objective 2 Examples Determine the domain and range of each relation from its graph. 2a. y = x - 2 2b. y = x2 - 4 2 y 2 4 4 6 –2 –2 –4 x 2 2 4 4 –2 –4 –2 –4 x y Figure 3.4 2 2 4 4 6 –2 y 2 –2 y Figure 3.5
hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above