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Questions and Answers of College Algebra

Use the graph of the function to solve each equation or inequality.(a) ƒ(x) > 0 (b) ƒ(x) ≤ 0 y = f(x) 1 х
Fill in the blank(s) to correctly complete each sentence.A polynomial function with leading term 3x5 has degree __________.
Fill in the blank(s) to correctly complete each sentence, or answer the question as appropriate.For k > 0, if y varies directly as x, then when x increases, y______, and when x decreases, y_______.
Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once.A. The x-intercept is (-3, 0).B. The y-intercept is (0, 5).C. The
Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once.A. The x-intercept is (-3, 0).B. The y-intercept is (0, 5).C. The
The federal government has developed the body mass index (BMI) to determine ideal weights. A person’s BMI is directly proportional to his or her weight in pounds and inversely proportional to the
The force needed to keep a car from skidding on a curve varies inversely as the radius r of the curve and jointly as the weight of the car and the square of the speed. It takes 3000 lb of force to
Solve each problem.Find all zeros of ƒ(x) = x4 - 3x3 - 8x2 + 22x - 24, given that 1 + i is a zero.
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = 24x3 + 80x2 + 82x + 24
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = x4 + 3x3 - 3x2 - 11x - 6
Several graphs of the quadratic function ƒ(x) = ax2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F.a > 0; b2 - 4ac = 0 A.
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. f(x) = = 4x + 25 x +9
The period of a pendulum varies directly as the square root of the length of the pendulum and inversely as the square root of the acceleration due to gravity. Find the period when the length is 121
Solve each problem.Find a polynomial function ƒ of degree 3 with -2, 1, and 4 as zeros, and ƒ(2) = 16.
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = 3x4 - 7x3 - 6x2 + 12x + 8
Several graphs of the quadratic function ƒ(x) = ax2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F.a > 0; b2 - 4ac > 0
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. x² + 1 f(x) x² + 9
For each polynomial function, use the remainder theorem to find ƒ(k). f(x) = 6x4 + x 8x + 5x+6; k= - IN
For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = x4 + 6x3 + 9x2 + 3x - 3; k = 4
The sports arena in Exercise 43 requires a horizontal beam 16 m long, 24 cm wide, and 8 cm high. The maximum load of such a horizontal beam that is supported at both ends varies directly as the width
Solve each problem.Find a polynomial function ƒ with real coefficients of degree 4 with 3, 1, and -1 + 3i as zeros, and ƒ(2) = -36.
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.ƒ(x) = 15x3 + 61x2 + 2x - 8
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.Zero of 2 and zero of 4 having multiplicity 2; ƒ(1) = -18
A rock is projected directly upward from ground level with an initial velocity of 90 ft per sec.(a) Give the function that describes the height of the rock in terms of time t.(b) Determine the time
Work each problem.Suppose m varies directly as p2 and q4. If p doubles and q triples, what happens to m?
Identify any vertical, horizontal, or oblique asymptotes in the graph of y = ƒ(x). State the domain of ƒ. -3 3
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = x2 - 4x + 5; k = 2 - i
Show that the real zeros of each polynomial function satisfy the given conditions.ƒ(x) = x4 + x3 - x2 + 3; no real zero less than -2
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.Zero of 0 and zero of 1 having multiplicity 2; ƒ(2) = 10
One campus of Houston Community College has plans to construct a rectangular parking lot on land bordered on one side by a highway. There are 640 ft of fencing available to fence the other three
Identify any vertical, horizontal, or oblique asymptotes in the graph of y = ƒ(x). State the domain of ƒ. -3 -3 -1 3 -4
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = x2 + 3x + 4; k = 2 + i
Show that the real zeros of each polynomial function satisfy the given conditions.ƒ(x) = x5 + 2x3 - 2x2 + 5x + 5; no real zero less than -1
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.Zero of -4 and zero of 0 having multiplicity 2; ƒ(-1) = -6
A farmer wishes to enclose a rectangular region bordering a river with fencing, as shown in the diagram. Suppose that x represents the length of each of the three parallel pieces of fencing. She has
Identify any vertical, horizontal, or oblique asymptotes in the graph of y = ƒ(x). State the domain of ƒ. -3 3 -6 3.
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = x2 - 3x + 5; k = 1 - 2i
Show that the real zeros of each polynomial function satisfy the given conditions.ƒ(x) = 3x4 + 2x3 - 4x2 + x - 1; no real zero greater than 1
Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated.5 + i and 5 - i
A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting 2-in. squares from each corner and folding up the sides. Let x represent the width (in
Graph each rational function. f(x)
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). 3 f(x) = 4x4 + x² + 17x + 3; k = -
Show that the real zeros of each polynomial function satisfy the given conditions.ƒ(x) = 3x4 + 2x3 - 4x2 + x - 1; no real zero less than -2
Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated.7 - 2i and 7 + 2i
A piece of sheet metal is 2.5 times as long as it is wide. It is to be made into a box with an open top by cutting 3-in. squares from each corner and folding up the sides. Let x represent the width
Graph each rational function. х — 5 x + 3 f(x)
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). 4 3x4 + 13x3 – 10x + 8; k = 3 len |
Show that the real zeros of each polynomial function satisfy the given conditions.ƒ(x) = x5 - 3x3 + x + 2; no real zero greater than 2
Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated.0, i, and 1 + i
If a person shoots a free throw from a position 8 ft above the floor, then the path of the ball may be modeled by the parabolawhere v is the initial velocity of the ball in feet per second, as
Graph each rational function. x + 2 f(x) =
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = x3 + 3x2 - x + 1; k = 1 + i
Show that the real zeros of each polynomial function satisfy the given conditions.ƒ(x) = x5 - 3x3 + x + 2; no real zero less than -3
Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated.0, -i, and 2 + i
If a person shoots a free throw from an underhand position 3 ft above the floor, then the path of the ball may be modeled byRepeat parts (a) and (b) from Exercise 63. Then compare the paths for the
Graph each rational function. f(x) = x + 4
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = 2x3 - x2 + 3x - 5; k = 2 - i
Find a polynomial function f of least degree having the graph shown. (0, 30) -6
Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated.1 + √2, 1 - √2, and 1
Find two numbers whose sum is 20 and whose product is the maximum possible value.
Graph each rational function. 4 — 2х f(x) 8 — х
The remainder theorem indicates that when a polynomial ƒ(x) is divided by x - k, the remainder is equal to ƒ(k). For ƒ(x) = x3 - 2x2 - x + 2, use the remainder theorem to find each of the
Find a polynomial function f of least degree having the graph shown. (0, 9) -5
Find two numbers whose sum is 32 and whose product is the maximum possible value.
Graph each rational function. 6 — Зх f(x) 4 — х
The remainder theorem indicates that when a polynomial ƒ(x) is divided by x - k, the remainder is equal to ƒ(k). For ƒ(x) = x3 - 2x2 - x + 2, use the remainder theorem to find each of the
Find a polynomial function f of least degree having the graph shown. х (0, –1)
Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated.2 - i, 3, and -1
If an object is projected upward from ground level with an initial velocity of 32 ft per sec, then its height in feet after t seconds is given by s(t) = -16t2 + 32t. Find the number of seconds it
Graph each rational function. f(x) x2 — х — 2 Зх
The remainder theorem indicates that when a polynomial ƒ(x) is divided by x - k, the remainder is equal to ƒ(k). For ƒ(x) = x3 - 2x2 - x + 2, use the remainder theorem to find each of the
Find a polynomial function f of least degree having the graph shown. (0, 2) -1
Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated.3 + 2i, -1, and 2
If an object is projected upward from an initial height of 100 ft with an initial velocity of 64 ft per sec, then its height in feet after t seconds is given by s(t) = -16t2 + 64t + 100. Find the
Graph each rational function. 2х + 1 f(x) : x2 + 6х + 8
The remainder theorem indicates that when a polynomial ƒ(x) is divided by x - k, the remainder is equal to ƒ(k). For ƒ(x) = x3 - 2x2 - x + 2, use the remainder theorem to find each of the
Find a polynomial function f of least degree having the graph shown. A(0, 81) 40 -3 3
Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated.2 and 3 + i
The average price in dollars of a pound of chocolate chip cookies from 2002 to 2013 is shown in the table.The data are modeled by the quadratic function ƒ(x) = 0.0095x2 - 0.0076x + 2.660, where x =
Graph each rational function. 5x f(x) : x2 – 1
Graph each rational function. Зx2 + 3x — 6 х2 — х — 12 f(x) =
Work each problem.Find a value of c so that y = x2 - 10x + c has exactly one x-intercept.
Graph each rational function. (x + 4)² | f(x) : (x- (x – 1)(x + 5)
Show that the real zeros of each polynomial function satisfy the given conditions.ƒ(x) = 2x5 - x4 + 2x3 - 2x2 + 4x - 4; no real zero greater than 1
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k).ƒ(x) = x2 - 2x + 2; k = 1 - i
Identify any vertical, horizontal, or oblique asymptotes in the graph of y = ƒ(x). State the domain of ƒ. 1. -3
Work each problem.Suppose p varies directly as r3 and inversely as t2. If r is halved and t is doubled, what happens to p?
Solve each problem. Give approximations to the nearest hundredth.A toy rocket (not internally powered) is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). 2; k%3 f(x) 16х4 + 3x? — —
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.Zero of -3 having multiplicity 3; ƒ(3) = 36
Identify any vertical, horizontal, or oblique asymptotes in the graph of y = ƒ(x). State the domain of ƒ. -8- -8 4 8 4) |-- |
Work each problem.Suppose y is inversely proportional to x, and x is tripled. What happens to y?
In each scatter diagram, tell whether a linear or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, tell whether the
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.Zeros of 2, -3, and 5; ƒ(3) = 6
Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given.ƒ(x) = x5 + 2x4 + x3 + 3; -1.8 and -1.7
Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). f(x) = 5x4 + 2.x³ – x + 3; k = 5
Identify any vertical, horizontal, or oblique asymptotes in the graph of y = ƒ(x). State the domain of ƒ. х -8 -4
Work each problem.Suppose y is directly proportional to x, and x is replaced by 1/3 x. What happens to y?
In each scatter diagram, tell whether a linear or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, tell whether the
For each polynomial function, (a) list all possible rational zeros, (b) find all rational zeros, and (c) factor ƒ(x) into linear factors.Zeros of -2, 1, and 0; ƒ(-1) = -1

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