Exam 1: Functions, Graphs, and Models; Linear Functions

The population of a small town can be modeled by P $P = - 33 t + 12,800$ , where t is the number of years since 2010. Interpret the slope of the graph of this function as a rate of change.

Graph the function with a graphing utility. - $y = \frac { - 4 } { x - 6 }$

Provide an appropriate response. -If the ordered pair $( 6,2 )$ belongs to function $g$ , then $gـــــــ ( \quad ) =ـــــــ$

Graph the equation. - $y = - 3$

The function $\mathrm { E } ( \mathrm { x } ) = 0.0036 \mathrm { x } ^ { 3 } + 0.0055 \mathrm { x } ^ { 2 } + 0.19 \mathrm { x } + 1.76$ gives the approximate total earnings of a company, in millions of dollars, where $x = 0$ corresponds to $2006 , x = 1$ corresponds to 2007 , and so on. This model is valid for the years from 2006 to 2010 . Determine the earnings for 2007. Round to two decimal places if necessary.

Explain why the order in which coordinates are subtracted to find slope does not matter as long as x-coordinates are subtracted in the same order as y-coordinates.