Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Graphs of the Circular Functions - Section 4.2 Translations of the Graphs of the Sine and Cosine Functions - 4.2 Exercises - Page 160: 15



Work Step by Step

RECALL: The graph of $y=c+a\cdot\cos{x}$ involves a either a vertical shift of $c$ units upward (when $c\gt0$) or $|c|$ units downward when $c\lt0$ of the parent function $f(x)=\cos{x}$. The given function, $y=1+\cos{x}$, has $c=1$ so it involves a $1$-unit shift upward of the parent function $f(x)=\cos{x}$. Recall that the graph of $y=\cos{x}$ contains the points $(0, 1), (\pi, -1),$ and $(2\pi, 1)$. This means that when the graph of $f(x)=\cos{x}$ is shifted $1$ unit upward, the resulting graph contains the points $(0, 2), (\pi, 0),$ and $(2\pi, 2)$. Note that the only graph among thae choices that contains the three points above is the one in Option $I$.
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