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Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) $ f(x) = \log_2 x $(b) $ g(x) = \sqrt[4]{x} $(c) $ h(x) = \frac{2x^3}{1 - x^2} $ (d) $ u(t) = 1-1.1t + 2.54t^2 $ (e) $ v(t) = 5^t $ (f) $ w(\theta) = \sin \theta \cos^2 \theta $

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02:15

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 2

Mathematical Models: A Catalog of Essential Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Johns Hopkins University

Missouri State University

Harvey Mudd College

University of Nottingham

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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all right, we're going to classify each function, and some of them are pretty obvious and don't need a whole lot of explanation. So looking at a we have f of X equals log base two of X so clearly that one is longer with Mick, since it involves a LA Guerry them B. We have the four through to vex, since that involves a route that would be a root function and c, we have a polynomial over a polynomial, so we have a ratio of pollen or meals, and when you have a ratio of polynomial is it's called a rational function for D. We have a polynomial. We have constants and coefficients that are really numbers, and we have exponents that are integers or whole numbers. And so this one has degree to because the highest exponents is too. For party, we have a function of the form f of X equals B to the X, where B is a constant. So five is our constant raised to a variable power, so that would be known as an exponential function when the exponents is your variable and then we see in F some trig functions. So this one is triggered a metric

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