Stitz-Zeager_College_Algebra_e-book

This one x value divides the number line into two 3

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Unformatted text preview: graph of f if and only if f (a) = b. In other words, a generic point on the graph of y = f (x) is (x, f (x)), and a generic 2.4 Inequalities 155 point on the graph of y = g (x) is (x, g (x)). When we seek solutions to f (x) = g (x), we are looking for values x whose y values on the graphs of f and g are the same. In part 1, we found x = 3 is the solution to f (x) = g (x). Sure enough, f (3) = 5 and g (3) = 5 so that the point (3, 5) is on both graphs. We say the graphs of f and g intersect at (3, 5). In part 2, we set f (x) < g (x) and solved to find x < 3. For x < 3, the point (x, f (x)) is below (x, g (x)) since the y values on the graph of f are less than the y values on the graph of g there. Analogously, in part 3, we solved f (x) > g (x) and found x > 3. For x > 3, note that the graph of f is above the graph of g , since the y values on the graph of f are greater than the y values on the graph of g for those values of x. y y 8 8 7 7 6 y = f (x) 6 y = g (x) 5 5 4 4 3 3 2 y = g (x) 2 y = f (x) 1 1 1 2 3 −1 f (x) < g (x) 4...
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