Trigonometry (10th Edition)

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

Appendix D - Graphing Techniques - Exercises: 6b

Answer

The graph of $y = F(x + h)$ will be the horizontal translation of $y = F(x)$ left-wise or right-wise by $h$-units. The graph of $y = F(x) + h$ is not the same as the graph of $y = F(x + h)$. The graph of $y = F(x) + h$ is the vertical translation of $y = F(x)$ upwards or downwards by $h$-units.

Work Step by Step

If the equation $y = F(x)$ is being changed to $y = F(x + h)$, for some real number $h$, the graph of $y = F(x + h)$ will be a translation of $y = F(x)$ left-wise or right-wise horizontally by $h$-units. The graph of $y = F(x) + h$ is not the same as the graph of $y = F(x + h)$. It is because, for some real number $h$, the graph of $y = F(x) + h$ will result in either a vertical translation of $h$ values up or down of the graph $y = F(x)$, whereas, the graph of $y = F(x + h)$ will result in either a horizontal translation of $h$ values left or right of the graph $y = F(x)$.
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