Exam 3: Polynomial and Rational Functions

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zero of $- 5$ having multiplicity 2 and zero of 10 having multiplicity $1 ; P ( 0 ) = - 250$

Solve the problem. -A rock is propelled upward from the top of a building 160 feet tall at an initial velocity of 48 feet per second. The function that describes the height of the rocket in terms of time $t$ is $s ( t ) = - 16 t ^ { 2 } + 48 t + 160$ . Determine the maximum height that the rock reaches.

Use the graph to answer the question. -Find the domain of the rational function graphed below.

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 3 ) ^ { 2 } - 8$

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. -

Solve the problem. Round your answer to two decimal places. -The weight W of an object on the Moon varies directly as the weight E on earth. A person who weighs 114 lb on earth weighs 22.8 lb on the Moon. How much would a 180-lb person weigh on The Moon?

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 4 } + 14 x ^ { 3 } + 44 x ^ { 2 } - 70 x - 245 ; k = - 7$ (multiplicity 2)

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 5 x ^ { 4 } + 2 x ^ { 3 } + 10 x - 4 ; - 2 \text { and } - 1$

Solve the problem. -Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 3 x ^ { 2 } - 204 x + 46$ , where $c$ is cost and $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost?

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 5 x - 5$

Find all rational zeros and factor f(x). - $f(x)=6 x^{3}+19 x^{2}+8 x-5$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 4 x ^ { 3 } + 2 x - 7 ; 1$ and 2

Solve the problem. -The pitch $P$ of a musical tone varies inversely as its wavelength $W$ . One tone has a pitch of 202 vibrations per second and a wavelength of $2.7 \mathrm { ft }$ . Find the wavelength of another tone that a pitch of 481 vibrations per second. Round to the nearest tenth.

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 2 - x } { x ^ { 2 } } \text { has an oblique asymptote. }$

Solve the problem. -The height of a box is 8 inches. The length is three inches more than the width. Find the width if the volume is 864 cubic inches.

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-5)^{2}+2$ Find the $x$ -intercepts.

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $4 - 3 i ; f ( x ) = x ^ { 2 } - 8 x + 25$

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = - 2 ; \mathrm { f } ( \mathrm { x } ) = 2 \mathrm { x } ^ { 5 } - 2 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 4$

Find the zeros of the polynomial function and state the multiplicity of each. - $\left( x ^ { 2 } + x - 12 \right) ^ { 4 } ( x - 1 + \sqrt { 7 } ) ^ { 3 }$

Answer the question -If y varies inversely as x, and x is halved, how is y changed?