Exam 3: Polynomial and Rational Functions

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

Find the domain and range of the quadratic function whose graph is described. -The vertex is $( 1 , - 13 )$ and the graph opens up.

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

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = - x ^ { 2 } ( x + 8 ) \left( x ^ { 2 } - 1 \right)$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = ( x + 7 ) ( x + 1 ) ( 5 x + 4 )$

Find the zeros of the polynomial function - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20$

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

Find the axis of symmetry of the parabola defined by the given quadratic function. - $y + 4 = ( x - 2 ) ^ { 2 }$

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

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = x ^ { 2 } - 2 x - 5$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - $f ( x ) = 7 x ^ { 3 } - 4 x ^ { 2 } + 9 x + 3$ ; between $- 1$ and 0

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } ( x + 8 ) \left( x ^ { 2 } - 1 \right)$

Solve the problem -You have 64 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.

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

Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. -Touches the $x$ -axis at 0 and crosses the $x$ -axis at 3 ; lies below the $x$ -axis between 0 and 3 .

Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. -Crosses the $x$ -axis at $- 2,0$ , and 4 ; lies below the $x$ -axis between $- 2$ and 0 ; lies above the $x$ -axis between 0 and 4 .

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = x ^ { 4 } \left( x ^ { 4 } + 2 \right) ( 6 x + 4 )$

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. - $f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 4 } ( x - 9 ) ^ { 3 }$

Solve the problem -The cost in millions of dollars for a company to manufacture $x$ thousand automobiles is given by the function $C ( x ) = 4 x ^ { 2 } - 32 x + 128$ . Find the number of automobiles that must be produced to minimize the cost.

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - $f ( x ) = - 4 x ^ { 3 } - 3 x ^ { 2 } + 2 x + 1$