EXAMPLE 12Video Example )Sketch the graph of y = (x - 3)“(x + 1)³(x – 1) by finding its intercepts and its limits as x → o and x → -o.SOLUTION)'-1) =Notice that since (x - 3)4 is positive, the function doesn't change sign at 3; thus the graph doesn't cross the x-axis at 3. The graph crosses the axis at -1 andThe y-intercept is f(0) = (-3)4and the x-intercepts are found by setting y = 0: x = 3, 1,When x is large positive, all three factors are positive, solim (x - 3)4(x + 1)3(x – 1) = 0.x→ のWhen x is large negative, the first factor is large positive and the second and third factors are both large negative solim(x - 3)4(x + 1)³(x – 1) = 0.x- -00Combining this information, we give a rough sketch of the graph in the figure below.y3Need Help?Read It

EXAMPLE 12 Video Example Sketch the graph of y = (x - 3)*(x + 1)(x - 1) by finding its intercepts and its limits as x - o and x + -0o. SOLUTION The y-intercept is (0) - (-3)( '-1) - setting y - 0: x - 3, 1, . Notice that since (x - 3)4 is positive, the function doesn't change sign at 3; thus the graph doesn't cross the x-axis at 3. The graph crosses the axis at -1 and and the x-intercepts are found When x is large positive, all three factors are positive, so lim (x - 3)(x + 1) (x - 1) = 0o When x is large negative, the first factor is large positive and the second and third factors are both large negative so lim (x - 3)*(x + 1)(x - 1) - co. Combining this Information, we give a rough sketch of the graph in the figure below. Need Help? L Read t

EXAMPLE 12 Video Example Sketch the graph of y = (x - 3)(x + 1)(x - 1) by finding its intercepts and its limits as x - o and x + -0o. SOLUTION The y-intercept is (0) - (-3)( '-1) - setting y - 0: x - 3, 1, . Notice that since (x - 3)4 is positive, the function doesn't change sign at 3; thus the graph doesn't cross the x-axis at 3. The graph crosses the axis at -1 and and the x-intercepts are found When x is large positive, all three factors are positive, so lim (x - 3)(x + 1) (x - 1) = 0o When x is large negative, the first factor is large positive and the second and third factors are both large negative so lim (x - 3)(x + 1)(x - 1) - co. Combining this Information, we give a rough sketch of the graph in the figure below. Need Help? L Read t

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 7E

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