Exam 2: Polynomial, Power, and Rational Functions

Solve the problem. - $\mathrm { A } ( \mathrm { x } ) = - 0.015 \mathrm { x } ^ { 3 } + 1.05 \mathrm { x }$ gives the alcohol level in an average person's blood $x$ hrs after drinking 8 oz of 100 -proof whiskey. If the level exceeds $1.5$ units, a person is legally drunk. Would a person be drunk after 5 hours?

State the power and constant of variation for the function, and then analyze it. - $f ( x ) = - \frac { 1 } { 7 } \sqrt [ 4 ] { x }$

Write the statement as a power function equation. Use k as the constant of variation. -The height h of a cone with a fixed volume varies inversely as the square of its radius r.

Solve the inequality. - $( 2 x - 3 ) \sqrt { x + 1 } < 0$

State the domain of the rational function. - $f ( x ) = \frac { 13 } { 15 - x }$

Solve the inequality. - $\frac { 5 x + 2 } { 3 x ^ { 2 } + 6 } > 0$

Solve the problem. -The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 28 t + 192$ . Determine the number of units to be sold in order for $P < 0$ (a loss is taken).

Use the Rational Zeros Theorem to write a list of all potential rational zeros - $f ( x ) = 3 x ^ { 3 } + 49 x ^ { 2 } + 49 x + 27$

Match the polynomial function graph to the appropriate zeros and multiplicities. -

Solve the problem. -The profit made when $\mathrm { t }$ units are sold, $\mathrm { t } > 0$ , is given by $\mathrm { P } = \mathrm { t } ^ { 2 } - 28 \mathrm { t } + 187$ . Determine the number of units to be sold in order for $\mathrm { P } > 0$ (a profit is made).

Find the requested function. -Find the polynomial function with leading coefficient $- 7$ ; degree 3 ; and $- 5,1$ , and 5 as zeros.

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - 4 x + 48$

Find the remainder when f(x) is divided by (x - k) - $f ( x ) = 6 x ^ { 4 } - 6 x ^ { 3 } - 5 x ^ { 2 } - 8 x + 8 ; k = 2$

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and leading coefficient. - $\mathrm { E } ( \mathrm { m } ) = \mathrm { mc } ^ { 2 }$

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - 3 x - 28$

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

Match the equation to one of the curves (for x ≥ 0). - $f ( x ) = 5 x ^ { 1 / 4 }$

Describe the end behavior of the polynomial function by finding - $f ( x ) = - 7 x ^ { 2 } + 4 x ^ { 3 } + 2 x - 8$

Solve the polynomial inequality. - $x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 \geq 0$

Solve the problem. -A coin is tossed upward with an initial velocity of $16 \mathrm { ft } / \mathrm { sec }$ . During what interval of time will the coin be at a height of at least $60 \mathrm { ft }$ ? $\left( \mathrm { h } = - 16 \mathrm { t } ^ { 2 } + \mathrm { v } _ { \mathrm { O } } \mathrm { t } + \mathrm { h } _ { \mathrm { O } } \right.$ . $)$