Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Appendix C - Functions - Page 435: 24

Answer

Refer to Graph I, it is NOT a function. The domain is $[0, \infty)$. The range is $(–\infty, \infty)$.

Work Step by Step

Refer to Graph I and by way of Vertical Line Test, it is NOT a function because each vertical line drawn will intersect the curve on the graph in more than one point. And, for any value of x, except for x = 0, there will be two values for y, e.g. when x = 1, y can be 1 or – 1 since its power of index is positive, so the equation $x = y^4$ does not define a function. The x-values of the points on the curve will include all the real numbers from $0$ to $\infty$. The domain is $[0, \infty)$. The y-values of the points on the curve will include all the real numbers between $–\infty$ and $\infty$. The range is $(–\infty, \infty)$.
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