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Problem 1 Medium Difficulty

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 $

Answer

(a) $f(x)=\log _{2} x$ is a logarithmic function.
(b) $g(x)=\sqrt[4]{x}$ is a root function with $n=4$
(c) $h(x)=\frac{2 x^{3}}{1-x^{2}}$ is a rational function because it is a ratio of polynomials.
(d) $u(t)=1-1.1 t+2.54 t^{2}$ is a polynomial of degree 2 (also called a quadratic function).
(e) $v(t)=5^{t}$ is an exponential function.
(f) $w(\theta)=\sin \theta \cos ^{2} \theta$ is a trigonometric function.

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Video Transcript

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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