Exam 3: Polynomial and Rational Functions

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12 = 0$

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

Find the slant asymptote, if any, of the graph of the rational function. - $h ( x ) = \frac { x ^ { 3 } + 9 } { x ^ { 2 } + 7 x }$

Determine the constant of variation for the stated condition. - $c$ varies directly as a and inversely as $b$ , and $c = 5$ when $a = 60$ and $b = 25$ .

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - $f ( x ) = - 10 x ^ { 7 } - 3 x ^ { 6 } - 1.5 x ^ { 5 } + 9 x ^ { 4 } + x + 6$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x ^ { 2 } - 10 x + 2 } { 14 x }$

Find the domain and range of the quadratic function whose graph is described. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 11 x ^ { 2 }$ , but which has its vertex at $( 3,9 )$ .

Divide using long division. - $\left( 2 x ^ { 4 } - 3 x ^ { 2 } + 6 x ^ { 3 } - 9 x \right) \div ( 2 x + 6 )$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 4$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 12 x + 7$

Determine whether the function is a polynomial function. - $f ( x ) = \sqrt [ 3 ] { x ^ { 4 } } - x ^ { 4 } + 2$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 8 x - 3$

Find the domain and range of the quadratic function whose graph is described. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = 5 x ^ { 2 }$ , but which has a minimum of 5 at $x = 2$ .

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end -A herd of moose is introduced to a wildlife refuge. The number of moose, $N ( t )$ , after $t$ years is described by the polynomial function $N ( t ) = - t ^ { 3 } + 25 t + 120$ . Use the Leading Coefficient Test to determine the graph's end behavior. What does this mean about what will eventually happen to the moose population?

Determine the constant of variation for the stated condition. -If $y$ varies directly as the square root of $x$ , and $y = 9$ when $x = 49$ , find $y$ when $x = 36$ .

Determine the constant of variation for the stated condition. -While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If a passenger experiences a force of 57.6 newtons when the car is moving at a speed of 40 kilometers per hour and the passenger has a mass of 40 kilograms, find the force a passenger experiences when the car is moving at 30 kilometers per hour and the passenger has a mass of 70 kilograms.

Divide using long division. - $\frac { 8 r ^ { 3 } - 46 r ^ { 2 } - 7 r - 30 } { r - 6 }$

Determine the constant of variation for the stated condition. - $y = 1.4$ when $x = 0.7$

Find the horizontal asymptote, if any, of the graph of the rational function. - $f ( x ) = \frac { 8 x } { 8 x + 7 }$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. -The concentration, in parts per million, of a particular drug in a patient's blood x hours after the drug is administered is given by the function $f ( x ) = - x ^ { 4 } + 10 x ^ { 3 } - 36 x ^ { 2 } + 48 x$ How many hours after the drug is administered will it be eliminated from the bloodstream.