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In this problem, you will follow the parts below to solve an inequality involving h(x) = x² - 45. X-15 First, factor h(x) into linear factors. Then use your factored form to answer the parts below. (a) Find the zeroes of the numerator. x = x = (smaller value) (larger value) (b) Find the zero of the denominator. Note: We could have also asked for the equation of the vertical asymptote. x = (c) Determine the sign of h(x) on each subinterval of the real number line where X1, X2, and X3 correspond to the three x values found in parts (a) and (b) ordered from smallest to largest. ---Select-- ÷ X1 ---Select-- ÷ X2 --Select--- = X3 ---Select--- = (d) Use the signs in part (c) to determine the solution for h(x) ≥0. Give your answer in interval notation.

In this problem, you will follow the parts below to solve an inequality involving h(x) = x² - 45. X-15 First, factor h(x) into linear factors. Then use your factored form to answer the parts below. (a) Find the zeroes of the numerator. x = x = (smaller value) (larger value) (b) Find the zero of the denominator. Note: We could have also asked for the equation of the vertical asymptote. x = (c) Determine the sign of h(x) on each subinterval of the real number line where X1, X2, and X3 correspond to the three x values found in parts (a) and (b) ordered from smallest to largest. ---Select-- ÷ X1 ---Select-- ÷ X2 --Select--- = X3 ---Select--- = (d) Use the signs in part (c) to determine the solution for h(x) ≥0. Give your answer in interval notation.

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter7: Equations And Inequalities In Two Variables
Section7.1: Rectangular Coordinate System And Linear Equations
Problem 46PS
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In this problem, you will follow the parts below to solve an inequality involving h(x) = x² - 45. X-15 First, factor h(x) into linear factors. Then use your factored form to answer the parts below. (a) Find the zeroes of the numerator. x = x = (smaller value) (larger value) (b) Find the zero of the denominator. Note: We could have also asked for the equation of the vertical asymptote. x = (c) Determine the sign of h(x) on each subinterval of the real number line where X1, X2, and X3 correspond to the three x values found in parts (a) and (b) ordered from smallest to largest. ---Select-- ÷ X1 ---Select-- ÷ X2 --Select--- = X3 ---Select--- = (d) Use the signs in part (c) to determine the solution for h(x) ≥0. Give your answer in interval notation.
Transcribed Image Text:In this problem, you will follow the parts below to solve an inequality involving h(x) = x² - 45. X-15 First, factor h(x) into linear factors. Then use your factored form to answer the parts below. (a) Find the zeroes of the numerator. x = x = (smaller value) (larger value) (b) Find the zero of the denominator. Note: We could have also asked for the equation of the vertical asymptote. x = (c) Determine the sign of h(x) on each subinterval of the real number line where X1, X2, and X3 correspond to the three x values found in parts (a) and (b) ordered from smallest to largest. ---Select-- ÷ X1 ---Select-- ÷ X2 --Select--- = X3 ---Select--- = (d) Use the signs in part (c) to determine the solution for h(x) ≥0. Give your answer in interval notation.
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