Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.2 Mathematical Models: A Catalog of Essential Functions - 1.2 Exercises - Page 33: 1


(a) Logarithmic (b) Root function (c) Rational function (d) Second-degree polynomial (e) Exponential function (f) Trigonometric function

Work Step by Step

(a) $f(x)=log_{2}x$ contains the base 2 logarithm operator, and thus is a logarithmic function. (b) $g(x)=\sqrt[4] x$ is the fourth root of x, and thus is a root function. (c) $h(x)=\frac{2x^3}{1-x^2}$ is the quotient of two polynomial functions, and thus is a rational function. (d) $u(x)=1-1.1t+2.54t^2$ has powers of $t$ multiplied by constants. The greatest power of $t$ present is 2, so the function is a second-degree polynomial. (e) $v(t)=5^t$ is the constant $5$ raised to the power of $t$, making this an exponential function. (f) $w(\theta)=sin \theta \hspace{1.5mm} cos^2 \theta$ contains the sine and cosine function, both trigonometric functions themselves, making $w(\theta)$ a trigonometric function.
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