Exam 4: Polynomials and Rational Functions

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. - $f ( x ) = - 2 x ^ { 3 } - 16 x ^ { 2 } + 30 x + 108 ; [ 0,1 ]$

As one approaches a certain sound source, the sound intensity in arbitrary units increases according to the following function of time: $F ( x ) = - \frac { 2 ( x - 3 ) ^ { 2 } + 3 ( x - 3 ) - 9 } { 2 ( x - 3 ) + 30 }$ . Starting at $x = 0$ , when the source of sound is first sensed, how much time elapses until maximum sound intensity is felt? Round the result to the nearest hundredth.

Use the remainder theorem and synthetic division to find f(k). - $k = 2 ; f ( x ) = 9 x ^ { 4 } + 10 x ^ { 3 } + 6 x ^ { 2 } - 6 x + 16$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 2 - x } { x ^ { 2 } } \text { has an oblique asymptote. }$

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

Give the equation of any oblique asymptotes. - $h ( x ) = \frac { 7 x - 6 } { 3 x ^ { 2 } - 5 x + 2 }$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=-3 x(x+1)^{2}(x-2)^{2}$

Determine which of the rational functions given below has the following feature(s). - $x$ -intercepts: $( 4,0 )$ and $( - 3,0 )$ , $y$ -intercepts: none, vertical asymptotes: $x = 0$ and $x = 1$ , horizontal asymptote: $y = 1$

The length of a table is 18 inches more than its width. If the area of the table is 3055 square inches, what is its length?

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

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. - $f ( x ) = - x ^ { 3 } - 8 x ^ { 2 } + 21 x + 108 ; [ 1,2 ]$

Use synthetic division to perform the division. $\frac { 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 } { x - 2 }$

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

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 2 } { x } + 3$

Find the zeros of the polynomial function and state the multiplicity of each. $f ( x ) = \left( x ^ { 2 } + x - 12 \right) ^ { 6 } ( x - 2 + \sqrt { 7 } ) ^ { 2 }$

A can has a surface area of 1118 square inches. Its height is 7.10 inches. What is the radius of the circular top? Round to the nearest hundredth.

Solve the problem. Round your answer to two decimal places. -The distance to the horizon varies directly as the square root of the height above ground level of the observer. If a person can see 6 miles from a height of 25 feet, how far can a person see from a height of 64 feet?

The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the intensity be at a distance of 5 miles? Round your answer to the nearest unit.