Exam 3: Polynomial and Rational Functions

Solve the problem. -The average round trip speed $S$ (in mph) of a vehicle traveling a distance of $d$ miles in each direction is given by $\mathrm { S } = \frac { 2 d } { \frac { d } { r _ { 1 } } + \frac { d } { r _ { 2 } } }$ where $r _ { 1 }$ and $r _ { 2 }$ are the rates of speed for the initial trip and the return trip, respectively. Suppose a motorist travels 100 miles to an event and averages 50 mph for the trip to the event. Determine the average speed necessary for the return trip if the motorist wants the average Speed for the round trip to be at least 60 mph. Round to one decimal place, if necessary.

Identify the vertex, axis of symmetry, and intercepts for the graph of the function. - $g ( x ) = - x ^ { 2 } + 6 x - 11$

Solve the inequality. Write the solution set in interval notation. - $\frac { t - 6 } { t ^ { 2 } + 4 } < 0$

Determine the vertical asymptote(s) of the graph of the function. - $f ( x ) = \frac { x } { x ^ { 2 } + 81 }$

Use synthetic division to divide the polynomials. - $\frac { x ^ { 5 } - 1,024 } { x - 4 }$

Solve the inequality. Write the solution set in interval notation. - $4 w ^ { 2 } > 4 w - 1$

Solve the inequality. Write the solution set in interval notation. - $\frac { x + 1 } { x - 2 } \leq 0$

Solve the problem. -The graph of $f ( x ) = \frac { 10 x ^ { 3 } + 8 } { 13 x ^ { 3 } }$ will behave like which function for large values of $| x |$ ?

The graph of y = f (x) is given. Solve the inequality. - $f ( x ) > 0$

Choose the one alternative that best completes the statement or answers the question. The graph of y = f (x) is given. Solve the inequality. - $f ( x ) \geq 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function defined by $f ( x ) = \frac { 1 } { x }$ is continuous.

Solve the problem. -The body mass index (BMI) of an individual varies directly as the weight of the individual and inversely as the square of the height of the individual. The body mass index for a 154 -lb person who is $71 \mathrm { in }$ . tall is $21.48$ . Determine the BMI for an individual who is $77 \mathrm { in }$ . tall and $164 \mathrm { lb }$ . Round to 2 decimal places.

Use synthetic division to divide the polynomials. - $\frac { 6 x ^ { 5 } + 16 x ^ { 4 } + 13 x ^ { 3 } + 23 x ^ { 2 } + 24 x - 4 } { x + 2 }$

Solve the problem. - $R$ varies directly as $x ^ { 2 }$ and inversely as $t$ when $R = 30$ when $x = 6$ and $t = 12$ . Find $R$ when $x = 7$ and $t = 9$ .

Solve the inequality. Write the solution set in interval notation. - $\frac { 7 } { 1 - x } \leq \frac { 2 } { 3 - x }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the graph of a polynomial function has 3 turning points, what is the minimum degree of the function?

Sketch the function. - $f ( x ) = - x ^ { 3 } - 3 x ^ { 2 }$

Solve the inequality. Write the solution set in interval notation. - $t ^ { 2 } - 8 t + 16 \geq 0$

Find the zeros of the function and state the multiplicities. - $f ( x ) = 2 x ^ { 5 } + 9 x ^ { 4 } + 7 x ^ { 3 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let $f ( x )$ be a polynomial. An inequality of the form $f ( x ) < 0 , f ( x ) > 0 , f ( x ) \geq 0$ , or $f ( x ) \leq 0$ is called aــــــــــــ inequality. If the polynomial is of degreeــــــــــــــ , then the inequality is also called a quadratic inequality.