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Classify each function as a power function, root function, polynomial (state its
Chapter 1, Problem 1(choose chapter or problem)
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) \(f(x)=\sqrt[5]{x}\)
(b) \(g(x)=\sqrt{1-x^{2}}\)
(c) \(h(x)=x^{9}+x^{4}\)
(d) \(r(x)=\frac{x^{2}+1}{x^{3}+x}\)
(e) \(s(x)=\tan 2 x\)
(f) \(t(x)=\log _{10} x\)
Questions & Answers
QUESTION:
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) \(f(x)=\sqrt[5]{x}\)
(b) \(g(x)=\sqrt{1-x^{2}}\)
(c) \(h(x)=x^{9}+x^{4}\)
(d) \(r(x)=\frac{x^{2}+1}{x^{3}+x}\)
(e) \(s(x)=\tan 2 x\)
(f) \(t(x)=\log _{10} x\)
ANSWER:Step 1 of 2
Power function: A function which is of the form \(f\left( x \right)=a{x^n}\), where \(n\) is an integer.
Root function: A function is of the form \(f\left( x \right)={x^{\frac{1}{n}}}\) where \(n\) is an integer.
Polynomial function: A polynomial function is of the form \(f\left( x \right)={a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + .......... + {a_0}\) where \(n\) is an integer.
Rational function: A rational function is in the form of the ratio of two polynomial functions.
\(f\left( x \right) = \frac{{g\left( x \right)}}{{h\left( x \right)}}\)
Here, \(h\left( x \right) \ne 0\).
Algebraic function: A function that is constructed by algebraic operations.
Trigonometric function: Trigonometric function is defined as functions of the angle of a triangle.
Eg; \(\cos \theta ,\;sin\theta\)