Single Variable Calculus, Chapter 1, 1.2, Section 1.2, Problem 1

Identify each function whether it is a power function, root function, polynomial(state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.




(a.) $f(x) = \sqrt[5]{x}$



The given function involves a radical sign.


$
\begin{equation}
\begin{aligned}
\boxed{ \text{So the function is a root function}} \
\end{aligned}
\end{equation}
$


(b.) $g(x) = \sqrt{1 - x^2}$

The given function involves an algebraic operation.
$\boxed { \text{So the function is an algebraic function}} $

(c.) $h(x) = x^9 + x^4$

The given function has a domain that have all possible values.
$\boxed { \text{So the function is a polynomial function with a degree of 9}} $

(d.) $\displaystyle r(x) = \frac{x^2 + 1}{x^3 + x}$

The given function shows the ratio of two polynomials.
$\boxed { \text{So the function is a rational function}} $

(e.) $\displaystyle s(x) = \tan 2x$

$\boxed {\text{The given function is a trigonometric function}} $

(f.) $t(x)= \log_{10} x $

$\boxed {\text{The given function is a logarithmic function} }$