Exam 2: Polynomial and Rational Functions

The total revenue $R$ earned per day (in dollars) from a pet-sitting service is given by $R ( p ) = - 12 p ^ { 2 } + 150 p$ where, $p$ is the price charged per pet (in dollars). Find the revenue when the price per pet is $\$ 4$ .

Use synthetic division to divide. $\left( 24 + 5 x ^ { 3 } + 22 x - 27 x ^ { 2 } \right) \div ( x - 2 )$

The height, $h ( x )$ , of a punted rugby ball is given by $h ( x ) = \frac { 1 } { 64 } x ^ { 2 } + \frac { 13 } { 32 } x + 2$ where x is the horizontal distance in feet from the point where the ball is punted. How far, horizon- tally, is the ball from the kicker when it is at its highest point?

Select the graph of the function $y = x ^ { 2 } - 5$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Write the complex number in standard form. $\sqrt { - 49 }$

Use the Remainder Theorem and synthetic division to find the function value. Verify your answers using another method. $h ( x ) = x ^ { 3 } - 6 x ^ { 2 } - 5 x + 7 , \quad h ( - 8 )$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } + 3 } { x }$

Use long division to divide. $\left( x ^ { 4 } + 9 x ^ { 3 } + 20 x ^ { 2 } - x - 5 \right) \div ( x + 5 )$

Perform the operation and write the result in standard form. $( 3 - 2 i ) ^ { 2 }$

Use synthetic division to divide. $\frac { x ^ { 3 } - 216 } { x - 6 }$

Select the correct graph of the function. $y = x ^ { 5 } - 7 x ^ { 3 } + 4 x$

The cost C (in millions of dollars) removing p% the industrial and municipal pollu- tants discharged into a river is given by $C = \frac { 245 p } { 100 - p } , 0 \leq p \leq 100$ Select the correct graph of the cost function.

Use Descartes' Rule of Signs to determine the possible number of positive and nega- tive zeros of $f ( x ) = x ^ { 5 } + 2 x$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 9 }$

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $- 7 + \sqrt { 6 } i$

Use Descartes' Rule of Signs to determine the possible number of positive and nega- tive zeros of $f ( x ) = 5 x ^ { 5 } + 10 x$

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 36 }$

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 25 x$

Find all the rational zeros of the function. $x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125$

Use long division to divide. $\left( x ^ { 3 } + 5 x ^ { 2 } + 16 x + 80 \right) \div ( x + 5 )$