Exam 2: Polynomial, Power, and Rational Functions

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = \frac { \sqrt { x + 9 } } { ( 2 x + 3 ) ( x - 2 ) }$

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. - $f ( x ) = ( 5 x + 1 ) \left( x ^ { 2 } + 2 \right) ( x - 6 )$

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. - $x + 2 ; 5 x ^ { 3 } + 8 x ^ { 2 } - 5 x + 2$

Solve the problem. -A retailer knows that $\mathrm { n }$ games can be sold in a month if the price is $30 - 0.2 \mathrm { n }$ dollars per game. If he buys each game for $\$ 14$ , and if he wishes to make a profit of at least $\$ 300$ per month on sales of this game, how many games must he sell each month?

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. - $k = - 3 ; f ( x ) = 4 x ^ { 3 } - 5 x ^ { 2 } + 2 x + 4 ;$ Lower bound?

Solve the problem. -An open-top rectangular box has a square base and it will hold 256 cubic centimeters (cc). Each side has length $x$ height $y \mathrm {~cm}$ . The box's surface area is given by $S ( x ) = \frac { 1024 } { x } + x ^ { 2 }$ Estimate the minimum surface area and the value of $x$ that will yield it.

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - $f ( x ) = - 19 - 15 x ^ { 4 } + 6 x - 2 x ^ { 3 } + 4 x ^ { 2 }$

Solve the problem. Round as appropriate. -The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 3 cm on a side is 81 g, find the weight of the liquid in a cubical container 4 cm on a side.

Match the graph of the rational function with its equation. -

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = 2 x ^ { 5 } + 9 x ^ { 4 } + 8 x ^ { 3 } - 44 x ^ { 2 } - 40 x + 10$

List the x- and y-intercepts, and graph the function. - $f(x)=\frac{3 x-5}{x-2}$

Write the word or phrase that best completes each statement or answers the question. Write a sentence that expresses the relationship in the formula, using the language of variation or proportion. - $\mathrm { P } = \frac { \mathrm { NkT } } { \mathrm { V } } \text {, where } \mathrm { P } \text { is the gas pressure of } \mathrm { N } \text { molecules in a volume } \mathrm { V } \text { at temperature } \mathrm { T }$

Find the zeros of the function. - $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 45 x + 126$

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - $f ( x ) = - 13 x ^ { 5 } - 4 x ^ { 4 } + 8$

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -1 and $2 - i$

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth. -

State how many complex and real zeros the function has. - $f ( x ) = x ^ { 2 } + 3 x + 9$

Write an equation for the linear function f satisfying the given conditions. - $f ( - 1 ) = - 5$ and $f ( 5 ) = 7$

Solve the inequality. - $\frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } + 11 x + 30 } < 0$

Find a cubic function with the given zeros. - $1,1 + \sqrt { 11 } , 1 - \sqrt { 11 }$