Trigonometry (10th Edition)

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

Appendix D - Graphing Techniques - Exercises - Page 446: 6a

Answer

If the equation $y = F(x)$ is changed to $y = c \cdot F(x)$, for some constant c, the graph of $y = F(x)$ will be stretched or shrank vertically.

Work Step by Step

To be more precise, if $c \gt 1$ or $|c| \gt 1$, the graph will be stretched vertically. if $0 \lt c \lt 1$ or $0 \lt |c| \lt 1$, the graph will be shrank vertically. if $-1 \lt c \lt 0$, the graph will be shrank vertically and reflected across the x-axis. if $c = -1$, the graph will be same without any stretching or shrinking but being reflected across the x-axis only. if $c \lt -1$, the graph will be stretched vertically and reflected across the x-axis.
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