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College Algebra Graphs and Models 5th edition Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna - Solutions

List all possible rational zeros of the function.a. f (x) = x5 - 3x2 + 1b. f (x) = x7 + 37x5 - 6x2 + 12c. f (x) = 2x4 - 3x3 - x + 8
For each polynomial function:a) Find the rational zeros and then the other zeros; that is, solve f (x) = 0.b) Factor f (x) into linear factors.1. f(x) = x3 + 3x2 - 2x - 62. f(x) = x3 - x2 - 3x + 33. f(x) = 3x3 - x2 - 15x + 5
Find only the rational zeros of the function. a. f(x) = x4 + 2x3 - 5x2 - 4x + 6 b. f(x) = x4 - 3x3 - 9x2 - 3x - 10 c. f(x) = x3 - x2 - 4x + 3
What does Descartes' rule of signs tell you about the number of positive real zeros and the number of negative real zeros of the function? 1. f(x) = 3x5 - 2x2 + x - 1 2. g(x) = 5x6 - 3x3 + x2 - x 3. h(x) = 6x7 + 2x2 + 5x + 4
Sketch the graph of the polynomial function. Follow the procedure outlined on p. 317. Use the rational zeros theorem when finding the zeros.a. f(x) = 4x3 + x2 - 8x - 2b. f(x) = 3x3 - 4x2 - 5x + 2c. f(x) = 2x4 - 3x3 - 2x2 + 3x
Determine the domain of the function.a.b.c.
Determine the vertical asymptotes of the graph of the function.a.b. c.
Determine the horizontal asymptote of the graph of the function.a.b. c.
Determine the oblique asymptote of the graph of the function.a.b. c.
Make a hand-drawn graph. Be sure to label all the asymptotes. List the domain and the x-intercepts and the y-intercepts. Check your work using a graphing calculator?a.b.c.
Use your knowledge of asymptotes and intercepts to match the equation with one of the graphs (a)-(f), which follow. List all asymptotes. Check your work using a graphing calculator.a) b) c)
Find a rational function that satisfies the given conditions, Answer may very, but try to give the simplest answer possible. a. Vertical asymptotes x = - 4, x = 5 b. Vertical asymptotes x = - 4, x = 5; horizontal asymptote y = 3/2, x-intercept (- 2, 0) c. Oblique asymptote y = x - 1
Vertical asymptote x = - 4, x = 5; x-intercept (- 2, 0)?
Vertical asymptotes x = - 4, x = 5; horizontal asymptote y = 3/2, x-intercept (- 2, 0)?
Oblique asymptote y = x - 1?
Medical Dosage.The functionGives the body concentration N(t), in parts per million, of a certain dosage of medication after time t, in hours.a) Graph of function on the interval [15, () and complete the following:b) Explain the meaning of the answer to part (a) in terms of the application.
Average Cost.The average cost per disc, in dollars, for a company to produce x discs on exercising is given by the functiona) Graph the function on the interval (0, () and complete the following: b) Explain the meaning of the answer to part (a) in terms of the application.
Population Growth.The population P, in thousands, of a senior community is given byWhere t is the time, in months.a) Graph the function on the interval [0, (] .b) Find the population at t = 0, 1, 3, and 8 months.c) Find the horizontal asymptote of the graph and complete the followingd) Explain the
Minimizing Surface Area.The Hold it Container Co. is designing an open top rectangular box, with a square base, that will hold 108 cubic centimeters.a) Express the surface area S as a function of the length x of a side of the base. b) Use a graphing calculator to graph the function on the interval
GraphUsing the same viewing window. Explain how the parabola y2 = x2 can be thought of as a nonlinear asymptote for y1?
Find the nonlinear asymptote of the function.a.b.
Graph the function.a.b.
For the function f(x) = x2 + 2x - 15, solve each of the following. a. f(x) = 0 b. f(x) < 0 c. f(x) ( 0
For the functionSolve each of the following.a. h(x) = 0b. h(x) ( 0c. h(x) ( 0
For the function g(x) = x5 - 9x3, solve each of the following. a. g(x) = 0 b. g(x) < 0 c. g(x) ( 0?
a. A related function is graphed. Solve the given inequality.x3 + 6x2b. x4 - 27x2 - 14x + 120 ( 0 c. 8x / x2 - 4 ( 0
List the critical values of the related function. Then solve the inequality.a.b.c.
For the functionSolve each of the following:a. g(x) = 0b. g(x) > 0c. g(x) ( 0
Temperature During an Illness.A person's temperature T, in degrees Fahrenheit, during an illness is given by the functionWhere t is the time since the onset of the illness, in hours. Find the interval on which the temperature was over 100o F.
Population Growth.The population P, in thousands, of a new senior community is given byWhere t is the time, in months. Find the interval on which the population was 40,000 or greater.
Total Profit. Flexl, Inc., determines that its total profit is given by the function P(x) = -3x2 + 630x - 6000. a) Flexl makes a profit for those nonnegative values of x for which P(x) > 0. Find the values of x for which Flexl makes a profit. b) Flexl loses money for those nonnegative values of x
Height of a Thrown Object.The function S(t) = - 16t2 + 32t + 1920Gives the height S, in feet, of an object thrown upward with a velocity of 32 ft>sec from a cliff that is 1920 ft high. Here t is the time, in seconds, that the object is in the air.a) For what times is the height greater than 1920
Number of Diagonals.A polygon with n sides has D diagonals, where D is given by the functionFind the number of sides n if27 ( D ( 230.
Number of Handshakes.If there are n people in a room, the number N of possible handshakes by all the people in the room is given by the functionFor what number of n people is66 ( N ( 300?
Find an equation for a circle satisfying the given conditions. a. Center: (- 2, 4); radius of length 3 b. Center: (0, - 3); diameter of length 7/2
a) Determine whether there is a maximum of minimum value and find that value.b) Determine whether there is a maximum or minimum value and find that value.c) Find the range?1. h(x) = - 2x2 + 3x - 82. g(x) = x2 - 10x + 2
Find the domain of the functiona.b.
Determine whether the statement is true or false. 1. The y-intercept of the graph of the function P(x) = 5 - 2x3 is 15, 02. 2. The degree of the polynomial x - 1/2x4 - 3x6 + x5 is 6. 3. If f(x) = (x + 7) (x - 8), then f(8) = 0.
Using the intermediate value theorem, determine, if possible, whether the function has at least one real zero between a and b. a. f (x) = x3 - 2x2 + 3; a = -2, b = 0 b. f (x) = x3 - 2x2 + 3; a = -1/2, b = 1
For the polynomial P(x) = x4 - 6x3 + x - 2 and the divisor d(x) = x - 1, use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x). Express P(x) in the form d(x) ( Q(x) + R(x)?
Use synthetic division to find the quotient and the remainder. a. (3x4 - x3 + 2x2 - 6x + 6) ( (x - 2) b. (x5 - 5) ( (x + 1)
Use synthetic division to find the function values.1. g(x) = x3 - 9x2 + 4x - 10 ; find g(-5)2. f (x) = 20x2 - 40x ; find f (½)3. f(x) = 5x4 + x3 - x; find f(- (2).
Using synthetic division, determine whether the numbers are zeros of the polynomial function?a. -3i, 3; f (x) = x3 - 4x2 + 9x - 36b. - 1,5; f(x) = x6 - 35x4 + 259x2 - 225
Factor the polynomial function f (x). Then solve the equation f (x) = 0. a) h(x) = x3 - 2x2 - 55x + 56 b) g(x) = x4 - 2x3 - 13x2 + 14x + 24.
How is the range of polynomial function related to the degree of the polynomial?
Is it possible for the graph of a polynomial function to have no y-intercept? no x-intercepts? Explain your answer?
Explain why values of a function must be all positive or all negative between consecutive zeros?
In synthetic division, why is the degree of the quotient 1 less than that of the dividend?
Find the zeros of the polynomial function and state the multiplicity of each? 1. f (x) = (x2 - 10x + 25)3 2. h(x) = 2x3 + x2 - 50x - 25. 3. g(x) = x4 - 3x2 + 2.
Match the function with one of the graphs (a)-(d), which follow.1. f (x) = x4 - x3 - 6x2 2. f(x) = 1 - (x - 1)3 (x + 2)2 3. f(x) = 6x3 + 8x2 - 6x - 8
Determine whether the statement is true or false. a. If f(x) = (x + a) (x + b) (x - c), then f(- b) = 0. b. The graph of a rational function never crosses a vertical asymptote. c. For the function g(x) = x4 - 8x2 - 9, the only possible rational zeros are 1, - 1, 3, and - 3?
Explain why the graph of a rational function cannot have both a horizontal asymptote and an oblique asymptote?
Use the leading term test to describe the end behavior of the graph of the function.a) f(x) = - ½ x4 + 3x2 + x - 6b) f(x) = x5 + 2x3 - x2 + 5x + 4
Find the zeros of the polynomial function and state the multiplicity of each. a. g(x) = (x - 2/3) (x + 2)3 (x - 5)2 b. f(x) = x4 - 26x2 + 25 c. h(x) = x3 + 4x2 + 9x - 36
Interest Compounded Annually. When P dollars is invested at interest rate i, compounded annually, for t years, the investment grows to A dollars, where A = P(1 + i)t. a) Find the interest rate i if $6250 grows to $6760 in 2 years. b) Find the interest rate i if $1,000,000 grows to $1,215,506.25 in
Cholesterol Level and the Risk of Heart Attack. The table below lists data concerning the relationship of cholesterol level in men to the risk of a heart attack. Cholesterol Level Number of Men per 100,000 Who Suffer a Heart Attack 100.......................30 200 ......................65 250
Using the intermediate value theorem, determine, if possible, whether the function f has a zero between a and b. a. f(x) = 4x2 - 5x - 3; a = 1, b = 2 b. f(x) = x3 - 4x2 + ½x + 2; a = - 1, b = 1
In each of the following, a polynomial P(x) and a divisor d(x) are given. Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x). Express P(x) in the form d(x) ( Q(x) + R(x). a. P(x) = 6x3 - 2x2 + 4x - 1, d(x) = x - 3 b. P(x) = x4 - 2x3 + x + 5, d(x) = x + 1
Use synthetic division of find the quotient and the remainder. a. (x3 + 2x2 - 13x + 10) ( (x - 5) b. (x4 + 3x3 + 3x2 + 3x + 2), ( (x + 2) c. (x5 - 2x) ( (x + 1)
Use synthetic division to find the indicated function value. a. f (x) = x3 + 2x2 - 13x + 10; f (-2) b. f (x) = x4 - 16; f (-2) c. f (x) = x5 - 4x4 + x3 - x2 + 2x - 100; f (-10).
Using synthetic division, determine whether the given numbers are zeros of the polynomial function.a. - i, - 5; f(x) = x3 - 5x2 + x - 5b. - 1, - 2; f(x) = x4 - 4x3 - 3x2 + 14x - 8c. 1/3, 1; f(x) = x3 - 4/3x2 - 5/3 + 2/3
Factor the polynomial f(x). Then solve the equation f(x) = 0.a. f (x) = x3 + 2x2 - 7x + 4b. f (x) = x3 + 4x2 - 3x - 18c. f (x) = x4 - 4x3 - 21x2 + 100x - 100
Find a polynomial function of degree of 3 with the given number as zeros. a. - 4, - 1, 2 b. - 3, 1 - i, 1 + i c. ½, 1 - (2, 1 + (2
Find a polynomial function of degree 4 with - 5 as a zero of multiplicity 3 and ½ as a zero of multiplicity 1.
Find a polynomial function of degree 5 with -3 as a zero of multiplicity 2, 2 as a zero of multiplicity 1, and 0 as a zero of multiplicity 2?
Suppose that a polynomial function of degree 5 with rational coefficients has the given zeros. Find the other zero(s).a. - 2/3, (5, 4 + ib. 0, 1 + (3, - (3c. - (2, ½, 1, 2?
Find a polynomial function of lowest degree with rational coefficients and the following as some of its zeros.a. (11b. - i, 6c. - 1, 4, 1 + i
List all possible rational zeros.a. h(x) = 4x5 - 2x3 + 6x - 12b. g(x) = 3x4 - x3 + 5x2 - x + 1c. f(x) = x3 - 2x2 + x - 24
For each polynomial functiona. Find the rational zeros and then the other zeros; that is, solve f(x) = 0.b. Factor f(x) into linear factor.1. f (x) = 3x5 + 2x4 - 25x3 - 28x2 + 12x2. f (x) = x3 - 2x2 - 3x + 63. f (x) = x4 - 6x3 + 9x2 + 6x - 10
Use a graphing calculator to graph the polynomial function. Then estimate the function's (a) Zeros, (b) Relative maxima, (c) Relative minima, and (d) Domain and range? 1. f(x) = - 2x2 - 3x + 6 2. f (x) = x3 + 3x2 - 2x - 6 3. f(x) = x4 - 3x3 + 2x2
What does Descartes' rule of signs tell you about the number of positive real zeros and the number of negative real zeros of each of the following polynomial functions? a. f (x) = 2x6 - 7x3 + x2 - x b. h(x) = -x8 + 6x5 - x3 + 2x - 2 c. g(x) = 5x5 - 4x2 + x - 1
Graph the function. Be sure to label all the asymptotes. List the domain and the x-and y-intercepts? a. f(x) = x2 - 5 / x + 2 b. f(x) = 5 / (x - 2)2 c. f(x) = x2 + - 6 / x2 - x - 20
Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible? a. Vertical asymptotes x = - 2, x = 3 b. Vertical asymptotes x = - 2, x = 3; horizontal asymptote y = 4; x-intercept (- 3, 0)
Medical Dosage.The functionGives the body concentration N(t), in parts per million, of a certain dosage of medication after time t, in hours. a) Find the horizontal asymptote of the graph and complete the following: b) Explain the meaning of the answer to part (a) in terms of the application?
Height of a Rocket. The function S(t) = -16t2 + 80t + 224 Gives the height S, in feet, of a model rocket launched with a velocity of 80 ft/sec from a hill that is 224 ft high, where t is the time, in seconds. a) Determine when the rocket reaches the ground. b) On what interval is the height greater
Population Growth.The population P, in thousands, of Novi is given byWhere t is the time, in months. Find the interval on which the population was 400,000 or greater?
Determine the domain of the functionA. (- (, 2) ( (2, 3) ( (3, () B. (- (, - 3) ( (- 3, 1) ( (1, () C. (- (, 2) ( (3, () D. (- (, - 3) ( (1, ()
Determine the vertical asymptotes of the functionA. x = 1, x = -2, and x = 4 B. x = -1, x = 2, x = -4, and x = 4 C. x = -1, x = 2, and x = -4 D. x = 4
The graph of f(x) = - 1/2x4 + x3 + 1 is which of the following?
Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic? 1. f (x) = 7x2 - 5 + 0.45x4 - 3x3 2. h(x) = - 25 3. g(x) = 6 - 0.5x
Express x3 - 1 as a product of linear factors?
Find k such that x + 3 is a factor of x3 + kx2 + kx - 15?
When x2 - 4x + 3k is divided by x + 5, the remainder is 33. Find the value of k?
Find the domain of the function.a.b. c.
Is it possible for a third-degree polynomial with rational coefficients to have no real zeros? Why or why not?
Explain and contrast the three types of asymptotes considered for rational functions?
Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial as constant, linear, quadratic, cubic, or quartic. a. f (x) = 2x3 + 6x2 - x4 + 11 b. h(x) = -4.7x + 29 c. Find the zeros of the polynomial function and state the multiplicity of
Use synthetic division to find the quotient and the remainder. Show your work. (3x3 - 12x + 7) ( (x - 5)
Use synthetic division to find P(-3) for P(x) = 2x3 - 6x2 + x - 4. Show your work?
Use synthetic division to determine whether -2 is a zero of f (x) = x3 + 4x2 + x - 6. Answer yes or no. Show your work?
Find a polynomial of degree 4 with -3 as a zero of multiplicity 2 and 0 and 6 as zeros of multiplicity 1?
Suppose that a polynomial function of degree 5 with rational coefficients has 1, (3, and 2 - i as zeros. Find the other zeros?
Find a polynomial function of lowest degree with rational coefficients and the following as some of its zeros. a. - 10, 3i b. 0,- (3, 1 - i
List all possible rational zeros.a. f (x) = 2x3 + x2 - 2x + 12b. h(x) = 10x4 - x3 + 2x - 5
For each polynomial function:a) Find the rational zeros and then the other zeros; that is, solve f (x) = 0.b) Factor f (x) into linear factors.1. f (x) = x3 + x2 - 5x - 52. f (x) = 2x4 - 11x3 + 16x2 - x - 63. f (x) = x3 + 4x2 + 4x + 16
What does Descartes' rule of signs tell you about the number of positive real zeros and number of negative real zeros of the following function? g(x) = - x8 + 2x6 - 4x3 - 1
Graph the function. Be sure to label all the asymptotes. List the domain and the x-and y-intercepts?a.b.
Find a rational function that has vertical asymptotes x = -1 and x = 2 and x-intercept 1-4, 02?
The function S(t) = -16t2 + 64t + 192 gives the height S, in feet, of a model rocket launched with a velocity of 64 ft/sec from a hill that is 192 ft high. a) Determine how long it will take the rocket to reach the ground. b) Find the interval on which the height of the rocket is greater than 240
The graph of f (x) = x3 - x2 - 2 is which of the following?

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