Exam 4: Polynomial and Rational Functions

Solve. -The concentration of a certain gas molecule in the atmosphere serves as an indicator of industrial 335) 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 (ppb), to the year. Year Concentration (ppb) 0 2.2 10 3.1 25 3.9 35 3.3 50 2.3 Determine the linear, quadratic, or cubic function that best fits the data.

Translate the given formula to an English phrase using the word "varies". - $\mathrm { y }$ varies directly as $\mathrm { z }$ and $\mathrm { y } = 150$ when $\mathrm { z } = 10$ . Find $\mathrm { y }$ when $\mathrm { z }$ is 16 .

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f ( x ) = ( x - 3 ) ^ { 2 } - 6$ Find the y-intercept.

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7$ and $1.8$

Solve the problem -The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.8 \mathrm { t }$ represents the yearly income (or loss) from a real estate investment, where $t$ is time in years. After what year does income begin to decline?

Solve the problem -A rock is propelled upward from the top of a building 210 feet tall at an initial velocity of 176 feet per second. The function that describes the height of the rocket in terms of time $t$ is $s ( t ) = - 16 t ^ { 2 } + 176 t + 210$ . Determine the time at which the rock reaches its maximum height.

Answer the question - $\text { How can the graph of } f ( x ) = \frac { 3 } { x + 19 } \text { be obtained from the graph of } y = \frac { 1 } { x } \text { ? }$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 20 }$

Find all rational zeros and factor f(x). - $f ( x ) = 12 x ^ { 3 } + 73 x ^ { 2 } + 5 x - 6$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 1 } { x ^ { 2 } } \text { is increasing on the interval } ( - \infty , 0 )$

Round your answer to two decimal places. -The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 128 g, find the weight of the liquid in a cubical container 3 cm on a side.

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. - $f ( x ) = - x ^ { 3 } - 10 x ^ { 2 } - 3 x + 54 ; [ - 1,0 ]$

Match the equation to the correct graph. - $y = - \frac { 1 } { 2 } ( x + 2 ) ^ { 2 } - 6$

Provide an appropriate response. -What is the domain of the graph?

Translate the given formula to an English phrase using the word "varies". - $\mathrm { f } - \mathrm { stop } = \frac { \mathrm { f } } { \mathrm { D } }$ , where $\mathrm { f } -$ stop is camera setting with a lens with focal length $\mathrm { f }$ and diaphragm opening D

Sketch the graph of the parabola. - $f ( x ) = ( x + 6 ) ^ { 2 }$

Translate the given formula to an English phrase using the word "varies". -What type of variation is suggested by the graph?

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. - $f ( x ) = - x ^ { 4 } + 26 x ^ { 2 } - 25 ; [ 3,4 ]$

2Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a<0;-4ac=0

Determine whether the statement is true or false. -If x - 3 is a factor of a polynomial f(x), then f(-3) = 0.