Exam 3: Polynomial and Rational Functions

Find the indicated intercept(s) of the graph of the function. -Is there $y$ -axis symmetry for the rational function $f ( x ) = \frac { - 9 x ^ { 2 } } { - 2 x ^ { 3 } - 2 }$ ?

Determine the maximum possible number of turning points for the graph of the function. -Suppose that a polynomial function is used to model the data shown in the graph below. For what intervals is the function decreasing?

Solve Problems Involving Joint Variation - $f$ varies jointly as s and the sum of $p$ and $t$ .

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

Solve Problems Involving Joint Variation - $r$ varies jointly as $s$ and the square of $n$ .

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = 6 x ^ { 3 } + 5 x ^ { 2 } - 9 x - 15$

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

Determine the constant of variation for the stated condition. - $y$ varies jointly as $x$ and $z$ . $y = 7.5$ when $x = 75$ and $z = 10$ . Find $y$ when $x = 55$ and $z = 10$ .

Divide using long division. - $\frac { - 9 x ^ { 3 } + 9 x ^ { 2 } + 16 x + 18 } { 3 x + 1 }$

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - $f ( x ) = x ^ { 6 } - 11$

x Find the range of the quadratic function. - $f ( x ) = - 7 ( x - 4 ) ^ { 2 } - 9$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 15 x - 11 }$

Determine the constant of variation for the stated condition. - $y$ varies directly as $z ^ { 2 }$ and $y = 96$ when $z = 4$ . Find $y$ when $z = 3$ .

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - $f ( x ) = 6 x ^ { 4 } + 5 x ^ { 3 } - 4 x ^ { 2 } + 3 x - 5$

Solve the problem. -The daily profit in dollars of a specialty cake shop is described by the function $\mathrm { P } ( \mathrm { x } ) = - 4 \mathrm { x } ^ { 2 } + 192 \mathrm { x } - 1904$ , where $x$ is the number of cakes prepared in one day. The maximum profit for the company occurs at the vertex of the parabola. How many cakes should be prepared per day in order to maximize profit?

Divide using synthetic division. - $\frac { 4 x ^ { 3 } - 18 x ^ { 2 } - 4 x - 30 } { x - 5 }$

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. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

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. - $f ( x ) = - 2 ( x - 4 ) ( x + 5 ) ^ { 3 }$

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - $f ( x ) = x ^ { 4 } + 5 x ^ { 3 } - 5 x ^ { 2 } + 4 x - 12$

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. - $f(x)=x^{2}+6 x+8$