Exam 4: Polynomials and Rational Functions

Determine which of the rational functions given below has the following feature(s). -x-intercepts: $( 3,0 )$ and $( 5,0 )$ , y-intercept: $( 0,15 )$ , vertical asymptote: $x = 1$ , horizontal asymptote: $y = 1$

Find the domain and range of the function. - $f ( x ) = 9 - x ^ { 2 }$

Find the zeros of the polynomial function and state the multiplicity of each. $f ( x ) = 9 x ^ { 6 } + x ^ { 4 }$

The following polynomial approximates the rabbit population in a particular area. $R ( x ) = - 0.135 x ^ { 5 } + 2.952 x ^ { 4 } + 3500$ where x is the number of years from year 0. Use a graphing calculator to describe the rabbit population from the years 0 to 25.

The polynomial $G ( x ) = - 0.006 x ^ { 4 } + 0.140 x ^ { 3 } - 0.53 x ^ { 2 } + 1.79 x$ measures the concentration of a dye in the bloodstream $x$ seconds after it is injected. Does the concentration increase between 14 and 15 seconds?

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 1 } { ( x - 7 ) ^ { 2 } } + 5$

The area of a square is numerically 21 more than the perimeter. Find the length of the side.

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 36$

Use the remainder theorem and synthetic division to find f(k). - $k = - 3 + 2 i ; f ( x ) = x ^ { 2 } - 5 x - 5$

If y varies inversely as the square of x, and x is tripled, how is y changed?

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative. -

A ball is thrown downward from a window in a tall building. Its position at time t in seconds is $\mathrm { s } ( \mathrm { t } ) = 16 \mathrm { t } ^ { 2 } + 32 \mathrm { t }$ where s(t) is in feet. How long (to the nearest tenth) will it take the ball to fall 106 feet?

Round to the nearest tenth unless indicated otherwise. -The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00, how much will a 20 foot length with diameter 5 inches cost? Round to the Nearest cent.

The height of a box is 4 inches. The length is three inches more than the width. Find the width if the volume is 352 cubic inches.

The population of a small town is given by the table. If the population is modeled $b y \mathrm { p } ( \mathrm { t } ) = \mathrm { at } { } ^ { 2 } + \mathrm { b }$ where $\mathrm { t }$ is in years and $\mathrm { t } = 0$ corresponds to the year 1980 and $t = 1$ corresponds the year 1990 , find $a$ .

Find an equation for the rational function graph. -

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 2,1,0$ and $P ( 2 ) = 40$

Identify the vertex of the parabola. - $y = x ^ { 2 } - 18 x + 85$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 2.54 x ^ { 4 } + 3 x ^ { 2 } + x - 2$

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = x ^ { 4 } - 26 x ^ { 2 } + 25 ; [ - 1,0.5 ]$