Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.3 - Analyzing Graphs of Functions - 2.3 Exercises - Page 194: 19

Answer

x = -3

Work Step by Step

Another word for zeros is the x-intercept. An x-intercept is where the line crosses the x-axis. For this to happen, the y-value must be 0, so to find the zeros of the function, the equation must equal 0. 0 = $\frac{x + 3}{2x^{2} - 6}$ Overall, we want to separate the x from all other constants. The first step would be to multiply $2x^{2} - 6$ from each side. 0 * $2x^{2} - 6$ = $\frac{(x + 3) * 2x^{2} - 6}{2x^{2} - 6}$ This gets: 0 = x + 3 We then want to subtract 3 from each side. 0 - 3 = x + 3 - 3 This gets: -3 = x Since x = -3 when y = 0, x = -3 is a zero of the function.
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