Chapter Problem Part of a computer graphic designer's job may be to create and manipulate electronic images found in video games. Power functions define curves that are useful in the design of characters, objects, and background scenery. Domain restrictions allow two or more curves to be combined to create a particular form. For example, a character's eye could be created using parabolas with restricted domains.

Describe the type$($s$)$ of power function$($s$)$ that could be used to design two of the following in a new video game. Provide equations and sketches of your functions. Include the domain and range of the functions you use.

the path of a river that extends from the southwest to the northeast part of a large forest

the cross$-$section of a valley that lies between two mountain ranges

a deep canyon where the river flows

characters' facial expressions

a lightning bolt

horseshoe tracks in the sand

Use the idea of this question to creat an own design, using at least four power functions in the process, make sure to write your equations as well asthe domain and ranges of each functions used. It isstrongly recommendend to use desmos for this task