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• Notes

Classify each function as a power function, root function,

polynomial (state its degree), rational function, algebraic function,
trigonometric function, exponential function, or logarithmic function.

1. (a) $f(x)=\log _{2} x \quad$ (b) $g(x)=\sqrt[4]{x}$

(c) $h(x)=\frac{2 x^{3}}{1-x^{2}} \quad$ (d) $u(t)=1-1.1 t+2.54 t^{2}$

(e) $v(t)=5^{t} \quad$ (f) $w(\theta)=\sin \theta \cos ^{2} \theta$

2. (a) $y=\pi^{x} \quad$ (b) $y=x^{\pi}$

(c) $y=x^{2}\left(2-x^{3}\right) \quad$ (d) $y=\tan t-\cos t$

(c) $y=\frac{s}{1+s} \quad$ (f) $y=\frac{\sqrt{x^{3}-1}}{1+\sqrt[3]{x}}$

(1) (a) logarithmic function
(b) Root function
(c) Rational Function

(d) Polynomial function (2)
(e) Exponential function
(f) Trigonometric fanction

(2) (a) Exponential function
(b) power function
(c) polynomial function (5)

(d) trigonometric and al gebraic
(e) Rational function
(f) Rational function

Find the domain of the function $f(x)=\frac{\cos x}{1-\sin (x)}$

$1-\sin (x)=0$
$1=\sin (x)$
$\sin (x)=1$

$x=\frac{\pi}{2}+2 n \pi, n$ integer

Domain $\left\{x \in R | x \neq \frac{\pi}{2}+2 n \pi , {\text { n intege }}\right\}$