Exam 3: Polynomial and Rational Functions

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. - $\frac{x+9}{x+2}<5$

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. - $\frac { 2 } { x - 7 } < 1$

Solve the problem. -The manufacturer of a CD player has found that the revenue $R$ (in dollars) is $R ( p ) = - 5 p ^ { 2 } + 1850 p$ , when the unit price is p dollars. If the manufacturer sets the price $p$ to maximize revenue, what is the maximum revenue to the nearest whole dollar?

Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. - $f(x)=(x-4)^{2}-3$

Solve Combined Variation Problems -P varies directly as the square of $R$ and inversely as the cube of $S$ .

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = 2 x ^ { 3 } - 13 x ^ { 2 } + 22 x - 8$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - x ^ { 2 } + 2 x + 1$

Graph the rational function. - $f ( x ) = \frac { x ^ { 2 } - 7 x + 12 } { ( x - 5 ) ^ { 2 } }$

Determine whether the function is a polynomial function. - $f ( x ) = 2 x ^ { 3 } + 5 x ^ { 2 } - 2 x ^ { - 5 } + 125$

Determine the constant of variation for the stated condition. -The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 25 minutes requires $12.5$ gallons of water. Find the amount of water used in a shower lasting 10 minutes.

Solve the problem. -April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 22 feet high. The height of the arrow is given by the function $h ( t ) = - 16 t ^ { 2 } + 64 t + 22$ , where $t$ is the time is seconds. What is the maximum height of the arrow?

Use the graph of the rational function shown to complete the statement. - As $x \rightarrow 3 ^ { - } , f ( x ) \rightarrow$ ?

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = ( x - 3 ) ( x - 2 ) ( x + 1 ) ^ { 2 }$

Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 8 - x ^ { 2 } - 2 x$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = 4 x ^ { 3 } - 2 x ^ { 3 } - x ^ { 5 }$

x Find the range of the quadratic function. - $f ( x ) = - x ^ { 2 } - 8 x - 9$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $x ^ { 3 } + 2 x ^ { 2 } - 5 x - 6 = 0$

Solve the problem. -An object is propelled vertically upward from the top of a 240 -foot building. The quadratic function $s ( t ) = - 16 t ^ { 2 } + 128 t + 240$ models the ball's height above the ground, $s ( t )$ , in feet, $t$ seconds after it was thrown. How many seconds does it take until the object finally hits the ground? Round to the nearest tenth of a second if necessary.

Graph the rational function. - $f ( x ) = \frac { x ^ { 4 } } { x ^ { 2 } + 25 }$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = ( 7 x - 6 ) ^ { 5 } \left( x ^ { 5 } - 1 \right) ( x + 1 )$