Exam 3: Polynomial and Rational Functions

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } + x + 6$

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $x ^ { 2 } + 8 x + 15 \geq 0$

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $x ^ { 3 } + 4 x ^ { 2 } - x - 4 > 0$

Determine the constant of variation for the stated condition. - $y$ varies directly as $x$ and inversely as the square of $z . y = 9$ when $x = 36$ and $z = 6$ . Find $y$ when $x = 88$ and $z = 5$ .

Find the vertical asymptotes, if any, of the graph of the rational function. - $h ( x ) = \frac { x + 5 } { x ^ { 2 } - 25 }$

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = x ^ { 2 } + 2 x - 6$

Divide using long division. - $\frac { x ^ { 4 } + 81 } { x - 3 }$

Find the slant asymptote, if any, of the graph of the rational function. - $h ( x ) = \frac { x ^ { 3 } + 8 } { x ^ { 2 } - 9 }$

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. - $x ^ { 3 } - 5 x ^ { 2 } + 2 x + 8 = 0 ; 2$

Use transformations of f(x) $f ( x ) = \frac { 1 } { x } \text { or } f ( x ) = \frac { 1 } { x ^ { 2 } }$ to graph the rational function. -

Use transformations of f(x) $f ( x ) = \frac { 1 } { x } \text { or } f ( x ) = \frac { 1 } { x ^ { 2 } }$ to graph the rational function. - $h ( x ) = \frac { 1 } { x + 3 }$

Graph the polynomial function. - $f(x)=7 x-x^{3}-x^{5}$

Graph the polynomial function. - $f ( x ) = x ^ { 4 } - 9 x ^ { 2 }$

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. - $\frac { x } { x + 3 } \geq 2$

Write an equation that expresses the relationship. Use k as the constant of variation. - $y = 2$ when $x = 3$

Solve the problem. -The perimeter of a rectangle is 44 feet. Describe the possible lengths of a side if the area of the rectangle is to be greater than 105 square feet.

Find the axis of symmetry of the parabola defined by the given quadratic function. - $y + 9 = ( x + 3 ) ^ { 2 }$

Write an equation that expresses the relationship. Use k as the constant of variation. - $y = 55$ when $x = 3$

Divide using long division. - $\left( x ^ { 2 } - 3 x - 18 \right) \div ( x - 6 )$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 2 } \left( x ^ { 2 } + 7 \right) ^ { 5 }$