208 CHAPTER 2 Graphs and Functions Five ordered pairs are 1-2, 02, 1-1, -32, 10, -42, 11, -32, and 12, 02. S Now Try Exercises 47(a), 51(a), and 53(a). (c) A table provides an organized method for determining ordered pairs. Here, we let x equal -2, -1, 0, 1, and 2 in y = x2 - 4 and determine the corresponding y-values. x y -2 0 -1 -3 0 -4 1 -3 2 0 y = 1-222 - 4 = 4 - 4 = 0 y = 1-122 - 4 = 1 - 4 = -3 y = 02 - 4 = -4 y = 12 - 4 = -3 y = 22 - 4 = 0 The graph of an equation is found by plotting ordered pairs that are solutions of the equation. The intercepts of the graph are good points to plot first. An x-intercept is a point where the graph intersects the x-axis. A y-intercept is a point where the graph intersects the y-axis. In other words, the x-intercept is represented by an ordered pair with y-coordinate 0, and the y-intercept is an ordered pair with x-coordinate 0. A general algebraic approach for graphing an equation using intercepts and point-plotting follows. x y y-intercept (0, y) (x, 0) x-intercept 0 Intercepts Graphing an Equation by Point Plotting Step 1 Find the intercepts. Step 2 Find as many additional ordered pairs as needed. Step 3 Plot the ordered pairs from Steps 1 and 2. Step 4 Join the points from Step 3 with a smooth line or curve. * Intercepts are sometimes defined as numbers, such as x-intercept 1 4 and y-intercept -1. In this text, we define them as ordered pairs, such as A1 4 , 0B and 10, -12. EXAMPLE 8 Graphing Equations Graph each equation discussed in Example 7. (a) y = 4x - 1 (b) x = 2y - 1 (c) y = x2 - 4 SOLUTION (a) Step 1 Let y = 0 to find the x-intercept, and let x = 0 to find the y-intercept. y = 4x - 1 0 = 4x - 1 Let y = 0. 1 = 4x Add 1. 1 4 = x Divide by 4. y = 4x - 1 y = 4102 - 1 Let x = 0. y = 0 - 1 Multiply. y = -1 Subtract. The intercepts are A1 4 , 0B and 10, -12.* Note that the y-intercept is one of the ordered pairs we found in Example 7(a).
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