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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

Write a polynomial f(x) in complete factored form that satisfies the conditions. Let the leading coefficient be 1.Degree 4; zeros: 2 with multiplicity 3, and 6 with multiplicity 1
Complete the following. (a) State the degree and leading coefficient of f. (b) State the end behavior of the graph of f. f(x) = 3x³-2-x²
The graph of either a cubic, quartic, or quintic polynomial f(x) with integer zeros is shown. Write the complete factored form of f(x). L 75 25 -75 2 y = f(x) 18 X
Complete the following. (a) State the degree and leading coefficient of f. (b) State the end behavior of the graph of f. f(x) = 4 + 2x - x²
Use synthetic division to divide the first polynomial by the second. x-x² + 3x²-x + ·lei
Write a polynomial f(x) in complete factored form that satisfies the conditions. Let the leading coefficient be 1.Degree 5; zeros: -2 with multiplicity 2, and 4 with multiplicity 3
Determine graphically any (a) Local extrema and (b) Absolute extrema. f(x) = -x + 4x² - 8
The data on the next page are modeled exactly by a linear, quadratic, cubic, or quartic function f with leading coefficient a. All zeros of f are real numbers located in the interval [-3,3]. (a)
Use the remainder theorem to find the remainder when f(x) is divided by the given x - k. f(x) = -4x² + 6x - 7 x + 4
The graph of either a cubic, quartic, or quintic polynomial f(x) with integer zeros is shown. Write the complete factored form of f(x). 150 50
Complete the following. (a) State the degree and leading coefficient of f. (b) State the end behavior of the graph of f. f(x) = -0.2x³+4x² - 3
The data on the next page are modeled exactly by a linear, quadratic, cubic, or quartic function f with leading coefficient a. All zeros of f are real numbers located in the interval [-3,3]. (a)
Determine graphically any (a) Local extrema and (b) Absolute extrema. f(x) 8 1 + x²
The data on the next page are modeled exactly by a linear, quadratic, cubic, or quartic function f with leading coefficient a. All zeros of f are real numbers located in the interval [-3,3]. (a)
The graph of either a cubic, quartic, or quintic polynomial f(x) with integer zeros is shown. Write the complete factored form of f(x). -2 2 y = f(x)
The graph of either a cubic, quartic, or quintic polynomial f(x) with integer zeros is shown. Write the complete factored form of f(x). y = f(x) 2 3 x
Use the remainder theorem to find the remainder when f(x) is divided by the given x - k. f(x) = 4x³ = x² + 4x + 2 x+2
Determine graphically any (a) Local extrema and (b) Absolute extrema. f(x) = 6 x² + 2x + 2
Use the remainder theorem to find the remainder when f(x) is divided by the given x - k. f(x) = -x² + 4x³ = x + 3 x-3
For each f(x), complete the following. (a) Find the x- and y-intercepts. (b) Determine the multiplicity of each zero of f. (c) Sketch a graph of y = f(x) by hand. f(x) = (x + 1)(x - 2)
Use the graph to determine if f is odd. even, or neither. y = f(x) x
The data on the next page are modeled exactly by a linear, quadratic, cubic, or quartic function f with leading coefficient a. All zeros of f are real numbers located in the interval [-3,3]. (a)
Use the figure to find the width W of the rectangle from its length and area A. Determine the value of W when x = 5 inches. W A=3x²³-5x² + 3x-5
For each f(x), complete the following. (a) Find the x- and y-intercepts. (b) Determine the multiplicity of each zero of f. (c) Sketch a graph of y = f(x) by hand. f(x) = -(x - 2)²
Use the graph to determine if f is odd. even, or neither. -2 Jr - y = f(x) 12
The data on the next page are modeled exactly by a linear, quadratic, cubic, or quartic function f with leading coefficient a. All zeros of f are real numbers located in the interval [-3,3]. (a)
For each f(x), complete the following. (a) Find the x- and y-intercepts. (b) Determine the multiplicity of each zero of f. (c) Sketch a graph of y = f(x) by hand. f(x) = -(x + 1)²
Use the graph to determine if f is odd. even, or neither. 2 -2 y = f(x) 11
For each f(x), complete the following. (a) Find the x-and y-intercepts. (b) Determine the multiplicity of each zero of f. (c) Sketch a graph of y = f(x) by hand. f(x) = (x - 1)³
Use Descartes' rule of signs to determine the possible number of positive and negative real zeros for each function. Then, use a graph to determine the actual numbers of positive and negative real
Use the graph to determine if f is odd. even, or neither. y = f(x) 2
Use Descartes' rule of signs to determine the possible number of positive and negative real zeros for each function. Then, use a graph to determine the actual numbers of positive and negative real
Determine if f is odd, even, or neither. f(x) = |x + 21
Determine if f is odd, even, or neither. f(x) X
Find the difference quotient of g. x = x + 1 = (x)8 I -
Use the graph to determine if f is odd. even, or neither. -2 y 2 77 y = f(x) 2
If possible, sketch a graph of a polynomial that satisfies the conditions. Let a be the leading coefficient.Degree 3 with three real zeros and a > 0
Determine if f is odd, even, or neither. f(x): = 1 x + 1
Evaluate f(x) at the given values of x. x = -2 and 1 10 y = f(x) 2
Use Descartes' rule of signs to determine the possible number of positive and negative real zeros for each function. Then, use a graph to determine the actual numbers of positive and negative real
Compare division of integers to division of polynomials. Give examples.
Find the difference quotient of g. x =(x)
If possible, sketch a graph of a polynomial that satisfies the conditions. Let a be the leading coefficient.Degree 4 with four real zeros and a < 0
Evaluate f(x) at the given values of x. x= -1, 0, and 3 4 2 y = f(x) 234
Use Descartes' rule of signs to determine the possible number of positive and negative real zeros for each function. Then, use a graph to determine the actual numbers of positive and negative real
When can you use synthetic division to divide two polynomials? Give one example where synthetic division can be used and one example where it cannot be used.
Use Descartes' rule of signs to determine the possible number of positive and negative real zeros for each function. Then, use a graph to determine the actual numbers of positive and negative real
The table is a complete representation of f. Decide if f is even, odd, or neither. x-100 -10 -1 56-23 f(x) 1 10 23 0 5 0 -5 100
If possible, sketch a graph of a polynomial that satisfies the conditions. Let a be the leading coefficient.Linear with a < 0
Use Descartes' rule of signs to determine the possible number of positive and negative real zeros for each function. Then, use a graph to determine the actual numbers of positive and negative real
Evaluate f(x) at the given values of x. x = -1, 1, and 2 -3-2 32 y = f(x) 1 2 3 ➤X
Complete the table if f is an even function. X f(x) -3 21 -2 -1 0 -25 1 2 -12 3
The table is a complete representation of f. Decide if f is even, odd, or neither. r -5 f(x) | −4 -4 -3 -2 -1 1 1 1 2 -2 3 -4
Solve for all real solutions. (a) Symbolically, (b) Graphically, and (c) Numerically. 2x²8x+6=0
Solve for all real solutions. (a) Symbolically, (b) Graphically, and (c) Numerically. x³ + x² - 6x = 0
Evaluate f(x) at the given values of x. x = -2, 0, and 2 23 y = f(x) ➤X
Complete the table if f is an odd function. x-5 f(x) 13 -3
Solve for all real solutions. (a) Symbolically, (b) Graphically, and (c) Numerically. 14-1=0
Evaluate f(x) at the given values of x. x = -4, 0, and 4 f(x) = -4x x³ + 2 4- x² if if-4 < x≤ 2 if x>2 x≤-4
Evaluate f(x) at the given values of x. x=-3, 1, and 4 x² - 4x² if f(x) = 3x² 1³-54 x=-3 if -3 < x < 4 if x = 4
Solve for all real solutions. (a) Symbolically, (b) Graphically, and (c) Numerically. x45x²+4=0 -
Solve for all real solutions. (a) Symbolically, (b) Graphically, and (c) Numerically. 6-4x2x² = 0
Solve for all real solutions. (a) Symbolically, (b) Graphically, and (c) Numerically. -x³ + 4x = 0
Complete the following. (a) Sketch a graph of f. (b) Determine if f is continuous on its domain. (c) Solve f(x) = 0. f(x) = (4-x² [x²-4 if -3 ≤x≤0 if 0
Evaluate f(x) at the given values of x. x = -2, 1, and 2 f(x) = x² + 2x + 6 if -5 ≤ x < 0 x + 6 if 0≤x < 2 x³ +1 if 2 ≤ x ≤5
Evaluate f(x) at the given values of x. x = 1975, 1980, and 1998 f(x) = 0.2(x - 1970)³ + 60 190 - (x - 1980)² 2(x - 1990) + 100 if 1970 ≤ x < 1980 if 1980 < x < 1990 if 1990 ≤ x ≤ 2000
Complete the following. (a) Sketch a graph of f. (b) Determine if f is continuous on its domain. (c) Solve f(x) = 0. f(x) = x+1 if -2 = x < 0 if 0≤x≤2
Complete the following. (a) Sketch a graph of f. (b) Determine if f is continuous on its domain. (c) Solve f(x) = 0. f(x) = (2x + 1 1-x² if-2 ≤x≤0 if 0
If the points (-5, -6) and (-3, 4) lie on the graph of an odd function f, then what do f(5) and f(3) equal?
Complete the following. (a) Sketch a graph of f. (b) Determine if f is continuous on its domain. (c) Solve f(x) = 0. f(x) = [x² if-1 ≤x≤1 xif 1 < x≤ 2
If the point (1 - a, b + 1) lies on the graph of an even function f, then what does f(a - 1) equal?
Complete the following. (a) Sketch a graph of f. (b) Determine if f is continuous on its domain. (c) Solve f(x) = 0. f(x) = [2 + x² (4-x² if-2 ≤ x
Solve the equation. Find all real solutions. - - 1 = 0
Sketch a graph of an odd linear function.
Solve the equation. Find all real solutions. 1²+8=0
Use the graph of f(x) = 4x - 1/3x3 and translations of graphs to sketch the graph of the equation. y = f(x)
Solve the equation. Find all real solutions. x²4 - 1 = 0
Solve the equation. Find all real solutions. 0= ل - ا = 0
Complete the following. (a) Sketch a graph of f. (b) Determine if f is continuous on its domain. (c) Solve f(x) = 0. f(x) = 2x -2 x²-2 T02 if -5 ≤ x < -1 if -1 ≤ x < 0 if 0≤x≤2
Does there exist a continuous odd function that is always increasing and whose graph passes through the points (-3,-4) and (2, 5)? Explain.
Use the graph of f(x) = 4x - 1/3x3 and translations of graphs to sketch the graph of the equation.
Complete the following. (a) Sketch a graph of f. (b) Determine if f is continuous on its domain. (c) Solve f(x) = 0. f(x) = x³ +3 x +3 if -2 ≤ x ≤0 if 4+x-xif 0
Solve the equation. Find all real solutions. 0 = px - x8
Complete the following. (a) Sketch a graph of f. (b) Determine if f is continuous on its domain. (c) Solve f(x) = 0. f(x) = 0.5r ²-4 4 if -4 ≤ x ≤-2 if -2 < x < 2 if 2 ≤ x ≤ 4
Use the graph of f(x) = 4x - 1/3x3 and translations of graphs to sketch the graph of the equation.
Sketch a graph of a continuous function with an absolute minimum of -3 at x = -2 and a local minimum of -1 at x = 2.
Is there an even function whose domain is all real numbers and that is always decreasing? Explain.
Sketch a graph of a continuous function with no absolute extrema but with a local minimum of -2 at x = -1 and a local maximum of 2 at x = 1.
Solve the equation. Find all real solutions. x³ - 25x = 0
Solve the equation. Find all real solutions. 162x³ = 0
Complete the following. (a) Sketch a graph of f. (b) Determine if f is continuous on its domain. (c) Solve f(x) = 0. f(x) = -2x x² +1 ³+1 if -3 ≤ x < -1 if-1 ≤x≤2 if 2
Sketch a graph of a continuous function that is increasing on (-∞, 2) and decreasing on (2, ∞). Could this function be quadratic?
Solve the equation. Find all real solutions. . + 7 = = = ,
Sketch a graph of a continuous function with a local maximum of 2 at x = -1 and a local maximum of 0 at x = 1.
Solve the equation. Find all real solutions. x² + 5 = 6x²
Solve the equation. Find all real solutions. 0 =zx9 - ع - *
An object is lifted rapidly into the air at a constant speed and then dropped. Its height h in feet after x seconds is listed in the table.(a) At what time does it appear that the object was
A water tank is filled with a hose and then drained. The table shows the number of gallons y in the tank after 1 minutes.The following function f models the data in the table.Solve the equation f(t)
A cylindrical container has a height of 16 centimeters. Water entered the container at a constant rate until it was completely filled. Then water was allowed to leak out through a small hole in the
Solve the equation. Find all real solutions. x² = x² = 2x² + 4

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