Exam 3: Polynomial and Rational Functions

Solve the problem. 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 15 foot length with diameter 6 inches cost? Round to the nearest cent.

Solve. -The concentration of a certain gas molecule in the atmosphere serves as an indicator of industrial air pollution. The data in the following table show the relationship of the estimated concentration of the molecule in the atmosphere, in parts per billion ( $\mathrm { ppb }$ ), to the year. Determine the linear, quadratic, cubic, or quartic function that best fits data.

Give the equatiosn of any horizontal asymptotes. - $h ( x ) = \frac { 7 - 5 x } { - 6 x + 7 }$

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 factor of f(x).

Solve the problem. -If an object is propelled upward from a height of 32 feet at an initial velocity of 80 feet per second, then its height after $t$ seconds is given by the equation $\mathrm { h } ( \mathrm { t } ) = - 16 \mathrm { t } ^ { 2 } + 80 \mathrm { t } + 32$ , where height is in feet. After how many seconds will the object reach a height of 132 feet?

Solve the problem. -A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is $s ( t ) = 16 t ^ { 2 } + 32 t$ , where $s ( t )$ is in feet. How long (to the nearest tenth) will it take the ball to fall 77 feet?

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 2 x ( x - 6 ) ( x + 11 )$

Solve the problem. Round to the nearest tenth unless indicated otherwise. -The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the Distance around the trunk is 3 feet, what is the volume of wood obtained from a tree that is 35 feet Tall having a measurement of 4 feet around the trunk?

Solve the problem. -The table shows the population of a city over the past five years. We used this data to develop the quadratic function $f ( x ) = 0.373 x ^ { 2 } + 0.165 x + 65$ , which models the population of the city $y$ in millions in the year $x$ , where $x = 0$ represents 2007. Use the model to find the estimated population in 2009 .

Solve the problem. Round your answer to two decimal places. -According to Ohmʹs law, the electric current I, in amperes, in a circuit varies directly as the voltage V. When 14 volts are applied, the current is 4 amperes. What is the current when 6 volts are Applied?

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 49 x + 196 ; k = 7$

Write the word or phrase that best completes each statement or answers the question. -Why does a function defined by a polynomial of degree five with real coefficients have either 1, 3, or 5 real zeros counting multiplicities?

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 3 } { x } \text { is an odd function. }$

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

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { 2 x + 2 } { 5 x - 7 }$

Find the zeros of the polynomial function and state the multiplicity of each. - $5 x ( x - 7 ) ^ { 3 } \left( x ^ { 2 } - 16 \right)$

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

Solve the problem. -The following polynomial approximates the shark population in a particular area. $R ( x ) = - 0.035 x ^ { 5 } + 3.785 x ^ { 4 } + 250$ , where $x$ is the number of years from year 0 . Use a graphing calculator to describe the shark population from the years 0 to 25 .

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 5 x + 14$

Answer the question -How can the graph of f(x) = 1x + 3 be obtained from the graph of y = 1x ?