Exam 4: Polynomial and Rational Functions

Sketch the graph of the rational function. - $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 9 }$

Find an equation for the rational function graph. -A plane suddenly experiences turbulence while in flight. At this point the change in its altitude, in feet, is represented by the following function of time: $\mathrm { F } ( \mathrm { x } ) = \frac { 4 ( x - 8 ) ^ { 2 } - 16 } { 16 ( x - 8 ) ^ { 2 } - 8 ( x - 8 ) + 9 }$ . Assuming that the turbulence first hits at time $x = 0$ , what is the maximum relative drop the plane will experience due to turbulence? (Round the result to the nearest hundredth.)

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = - 5 x ^ { 2 } ( x - 8 ) ( x + 2 ) ^ { 3 }$

Translate the given formula to an English phrase using the word "varies". - $A = \frac { 1 } { 2 } b h , \text { where } A \text { is the area of a triangle with base } b \text { and height } h$

Find the equation that the given graph represents. - $f ( x ) = x ^ { 3 } - 3$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 1 } { ( x - 4 ) ^ { 2 } } + 2$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 3 x ^ { 3 } + 42 x ^ { 2 } + 42 x + 27$

Graph the function. - $f ( x ) = - \frac { 1 } { x + 1 }$

Solve the problem -A ball is tossed upward. Its height after $\mathrm { t }$ seconds is given in the table. Time (seconds) 0.5 1 1.5 2 2.5 Height (feet) 26.5 39.5 44.5 41.5 30.5 Find a quadratic function to model the data. Use the model to determine when the ball reaches its maximum height, as well as the value of the maximum height.

Sketch the graph of the parabola. - $y=3(x-5)^{2}-1$

Solve the problem -A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Solve. -The student population of a small school has been increasing as shown in the following table. Year \# of Students 50 190 60 200 70 230 80 280 90 350 100 440 Determine the linear, quadratic, or cubic function that best fits the data.

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 1 }$

Find the equation that the given graph represents. - $f ( x ) = - x ^ { 3 } + 4$

Provide an appropriate response. -Find a quadratic function $\mathrm { f }$ having $\mathrm { x }$ -intercepts 3 and $- 4$ and $y$ -intercept $- 24$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $8 x ^ { 4 } + 15 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Provide an appropriate response. -What is the smallest possible degree of the function for which this graph represents?

Determine which of the rational functions given below has the following feature(s). -x-intercepts: $( - 5,0 )$ and $( - 3,0 ) , y$ -intercepts: $\left( 0 , \frac { 3 } { 5 } \right)$ , vertical asymptote: $x = 5$ , horizontal asymptote: $y = 1$

Solve the problem -A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting 2 cm squares from each corner and folding up the sides. Let x represent the width of the Original piece of cardboard. Find the width of the original piece of cardboard, x, if the volume of The box is 1152 cm3.

Determine whether the statement is true or false. -If f(x) is a polynomial having only real coefficients and 3 - 5i is a zero of f(x), then x - 3 - 5i is a factor of f(x).