Symmetry Determine whether the graphs of the following equations and functions are symmetric about the x-axis, the y-axis, or the origin. Check your work by graphing.
$\text{ƒ}\left(x\right)=x\mid x\mid$

Symmetry Determine whether the graphs of the following equations and functions are symmetric about the x-axis, the y-axis, or the origin. Check your work by graphing.

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=1$

Composition of even and odd functions from graphs Assume ƒ is an even function and g is an odd function. Use the (incomplete) graphs of ƒ and g  in the figure to determine the following function values. <IMAGE>

a. ƒ(g(-2))

Prove the following identities.

$\(\frac{\sin\theta}{1+\cos\theta}\)=\(\frac{1-\cos\theta}{\sin\theta}\)$

Prove the following identities.

$\(\tan\)2\(\theta\)=\(\frac{2\tan\theta}{1-\tan^2\theta}\)$

Parabola properties Consider the general quadratic function ƒ(x) = ax² + bx + c , with a ≠ 0.

a. Find the coordinates of the vertex of the graph of the parabola y= ƒ(x)  in terms of a, b, and c.

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\(\text{hr}\)$, which means its population is governed by the function $p\(\left\)(t\(\right\))=150\(\cdot{2^{\frac{t}{12}\)}}$, where $t$ is the number of hours after the first observation.

How long does it take the population to reach $10,000$?