Answer
(a) Logarithmic
(b) Root function
(c) Rational function
(d) Second-degree polynomial
(e) Exponential function
(f) Trigonometric function
Work Step by Step
(a) $f(x)=log_{2}x$ contains the base 2 logarithm operator, and thus is a logarithmic function.
(b) $g(x)=\sqrt[4] x$ is the fourth root of x, and thus is a root function.
(c) $h(x)=\frac{2x^3}{1-x^2}$ is the quotient of two polynomial functions, and thus is a rational function.
(d) $u(x)=1-1.1t+2.54t^2$ has powers of $t$ multiplied by constants. The greatest power of $t$ present is 2, so the function is a second-degree polynomial.
(e) $v(t)=5^t$ is the constant $5$ raised to the power of $t$, making this an exponential function.
(f) $w(\theta)=sin \theta \hspace{1.5mm} cos^2 \theta$ contains the sine and cosine function, both trigonometric functions themselves, making $w(\theta)$ a trigonometric function.
