Exam 3: Polynomial and Rational Functions

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The solution set for the inequality $( x + 10 ) ^ { 2 } \geq - 4$ is ـــــــ whereas the solution set for the inequality $( x + 10 ) ^ { 2 } \leq - 4$ is ــــــــــــــ

Solve the problem. -The following table represents the result of a synthetic division. Use $x$ as the variable. Identify the remainder.

Find the vertex of the parabola by applying the vertex formula. - $f ( x ) = - \frac { 1 } { 5 } x ^ { 2 } - 6 x - 7$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given the function defined by $h ( x ) = \frac { 1 } { 2 } x ^ { 5 } ( x + 0.6 ) ^ { 3 }$ , the value 0 is a zero with multiplicity , and the value -0.6 is a zero with multiplicity .

Graph the function. - $p ( x ) = \frac { 6 } { x ^ { 2 } - 16 }$

Sketch the function and determine the axis of symmetry. - $f ( x ) = 3 ( x - 1 ) ^ { 2 } + 6$

Find the vertex of the parabola. - $q ( x ) = 2 x ^ { 2 } - 12 x - 1$

Identify the vertex, axis of symmetry, and intercepts for the graph of the function. - $y = - x ^ { 2 } - 2 x + 8$

Identify the vertex and determine the minimum or maximum value of the function. - $f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7$

Use the factor theorem to factor the polynomial. -Factor $f ( x ) = 6 x ^ { 3 } + 31 x ^ { 2 } - 29 x + 6$ given that $\frac { 1 } { 3 }$ is a zero.

Identify the vertex, axis of symmetry, and intercepts for the graph of the function. - $g ( x ) = x ^ { 2 } - 2 x - 15$

Solve the problem. -Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop and go traffic. At higher speeds, the car must overcome more wind resistance. The variable x Given in the table represents the speed (in mph) for a compact car, and m(x) represents the gas mileage (in mpg). Use regression to find a quadratic function to model the data and then use the function to determine The speed with the greatest gas mileage. Round to the nearest mile per hour. Carry out all computations up to The final answer without rounding. x 25 30 35 40 45 50 55 60 65 m(x) 21.4 25.4 28.2 29.9 30.4 29.8 28 25.1 21

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The solutions to an inequality f (x) < 0 are the values of x on the intervals where f (x) is (positive/negative).

Identify the vertex and sketch the graph. - $f ( x ) = 2 x ^ { 2 } + 4$

Solve the problem. - $g ( x ) = - \frac { 1 } { 5 } x ^ { 6 } - 3$ a. Identify the power function of the form $y = x ^ { n }$ that is the parent function to the given graph. b. In order, outline the transformations that would be required on the graph of $y = x ^ { n }$ to make the Graph of the given function. c. Match the function with the graph. i. ii. iii. iv.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If y varies directly as two or more other variables such as x and w, then y = kxw, and we say that y varies as x and w.

Solve the inequality. Write the solution set in interval notation. - $\frac { 8 } { m - 9 } \geq 3$

Find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower bound theorem to limit your search for rational zeros. - $f ( x ) = 20 x ^ { 3 } - 47 x ^ { 2 } + 11 x + 6$

Solve the problem. -The resistance of a wire varies directly as its length and inversely as the square of its diameter. A 50 -ft wire with a $0.4$ -in. diameter has a resistance of $0.0125 \Omega$ . Find the resistance of a 20 -ft wire with a diameter of $0.1$ -in. Round to 4 decimal places if necessary.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Aـــــــــــ function is a function that can be written in the form $f ( x ) = \frac { p ( x ) } { q ( x ) }$ where $p ( x )$ and $q ( x )$ are polynomials, and $q ( x ) \neq 0$ .