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 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 172: 43

Answer

$f(x) = 1+tan~\frac{x}{2}$

Work Step by Step

We can see that this is the graph for a tangent function. Compared with a standard tangent function, the first positive asymptote occurs at $x = \pi$ instead of $\frac{\pi}{2}$. Therefore we need to include the term $\frac{x}{2}$ for the angle in the function. Compared with a standard tangent function, the y-values are translated upward by 1 unit. Therefore we need to include the term +1 in this function. The equation for this graph is: $f(x) = 1+tan~\frac{x}{2}$
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