Exam 3: Polynomial and Rational Functions

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x² should be positive or negative. -The height of a ball thrown from the ground, as a function of time.

Solve the problem. -x varies inversely as v, and x = 27 when v = 7. Find x when v = 21.

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x² should be positive or negative. -The amount of water in a pool as it is being filled, as a function of time.

Identify the vertex of the parabola. - $y = 4 x ^ { 2 } + 16 x + 12$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 2 x ^ { 3 } + 6 x ^ { 2 } + 12 x - 8$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x^{3}+7 x^{2}+11 x+5$

Solve the problem. -The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of The earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is 250 Miles above the earthʹs surface? Round your answer to the nearest hundredth of a pound.

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Solve the inequality. Write the solution set in interval notation. - $3 x ^ { 2 } + 7 x < 20$

Solve the problem. Round to the nearest tenth unless indicated otherwise. -The volume $V$ of a given mass of gas varies directly as the temperature $T$ and inversely as the pressure $\mathrm { P }$ . If $\mathrm { V } = 78.0$ in $^ { 3 }$ when $\mathrm { T } = 130 ^ { \circ }$ and $\mathrm { P } = 20 \mathrm { lb } / \mathrm { in } ^ { 2 }$ , what is the volume when $\mathrm { T } = 340 ^ { \circ }$ and $\mathrm { P } = 20 \mathrm { lb } / \mathrm { in } ^ { 2 }$ ?

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

Solve the problem. -Of all possible pairs of positive numbers having a sum of 78 , which pair has the maximum product?

Answer the question -What type of variation is suggested by the graph?

Match the equation to the correct graph. - $y = ( x + 5 ) ^ { 2 }$

Translate the given formula to an English phrase using the word ʺvariesʺ. - $\mathrm { A } = \pi \mathrm { r } ^ { 2 } \text {, where } \mathrm { A } \text { is the area of a circle of radius }$

Graph the function. - $f(x)=\frac{7}{x}$

Determine which of the rational functions given below has the following feature(s). - $x$ -intercepts: $- 2$ and $- 4$ , $y$ -intercepts: $\frac { 1 } { 2 }$ , vertical asymptote: $x = 4$ , horizontal asymptote: $y = 1$

Solve the problem. - $f(x)=-\frac{1}{2}(x-1)^{4}-4$

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$ -intercept?

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. - $f ( x ) = x ^ { 4 } - 13 x ^ { 2 } + 36 ; [ - 1,0.5 ]$