University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 11: 5

Answer

1. Domain: $(-\infty ,3)\cup (3,\infty )$ 2. Range: $(-\infty ,0)\cup (0,\infty )$

Work Step by Step

1. Remember, a rational function is only defined when its denominator part is not zero. We take the denominator of the function and compare it to zero to get the undefined points. $3-t=0$ $\Rightarrow t=3$ So, the function is undefined at $ t=3$. So it will be excluded from the domain as it yields zero in the denominator. Domain: $(-\infty ,3)\cup (3,\infty )$ 2. Since $y=\frac{4}{3-t}$, $y$ can obtain any value except zero, because $y$ is a fraction with any value in the denominator (except zero). Range: $(-\infty ,0)\cup (0,\infty )$
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