Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.2 - Mathematical Models: A Catalog of Essential Functions. - 1.2 Exercises - Page 34: 15


(a) The graph is on the figure below. (b) 1) the slope represents how many degrees Fahrenheit correspond to the change of temperature of one degree Celsius. 2) the intercept with $C$ axis says what is the temperature in Celsius when the temperature in Fahrenheit is $0$ 3) the intercept with $F$ axis says what is the temperature in Fahrenheit when the temperature in Celsius is $0$.

Work Step by Step

To sketch the graph first find the intercepts with the axes and then draw the line through the intercepts: 1) With $C$ axis for $F=0$ we have $$0=\frac{9}{5}C+32\Rightarrow \frac{9}{5}C=-32\Rightarrow C=\frac{160}{9}=17.78.$$ 2) With $F$ axis for $C=0$ we have $$F=\frac{9}{5}\cdot0+32=32.$$ The graph is shown in the figure below.
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