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Questions and Answers of College Algebra

Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Solve the equation.27 - (x - 4)3/2 = 0
Solve the equation. 3 = Vx + 2 + Vx – 1 х
Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window.ƒ(x) =
Use synthetic division to perform each division. x3 + x² +x x+i
Match each statement with its corresponding graph in choices A–D. In each case, k > 0.y varies inversely as x. (y = k/x) А. У В. У C. y D. — х х х х
Which function has a graph that does not have a horizontal asymptote? 2х — 7 x + 3 A. f(x) B. f(x) Зх x² – 9 x + 5 (x + 2)(x – 3) x² – 9 D. f(x) = С. f(х) x + 3
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.2x3 + x + 2; x + 1
Which function has a graph that does not have a vertical asymptote? 2х + 1 3 D. f(x) = x2 C. f(x) = B. f(x) = A. f(x) = - 8 2 x2 + 2
Graph each function. Determine the largest open intervals of the domain over which each function is (a) Increasing (b) Decreasing. f(x) = (x+3)4 - 3 1 3
Sketch the graph of an appropriate function and then use the graph to solve each equation or inequality. First determine whether the expression is an equation or an inequality. When appropriate, use
Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window.ƒ(x) =
Choices A–D below show the four ways in which the graph of a rational function can approach the vertical line x = 2 as an asymptote. Identify the graph of each rational function defined in parts
Use synthetic division to perform each division. 2 2 81
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.x3 + 2x2 + 3; x - 1
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing.ƒ(x) = (x - 1)4 + 2
After the numerator is divided by the denominator,(a) What is the oblique asymptote of the graph of the function?(b) Where does the graph of the function intersect its asymptote?(c) As x → ∞,
Repeat Exercise 47 if ƒ is the function whose graph is obtained by translating the graph of y = - 1/x2 to the left 3 units and up 1 unit.Exercise 47Let ƒ be the function whose graph is obtained by
Let ƒ be the function whose graph is obtained by translating the graph of y = 1/x to the right 3 units and up 2 units.(a) Write an equation for ƒ(x) as a quotient of two polynomials.(b) Determine
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. Зx2 — 6х — 24 бх — 24 %3D f(x) = 5x2 — 26х + 5
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. x2 — 2х — 3 f(x) = 2x? — х — 10
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. f(x) = x + 4 x-1
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. f(x) x - 1 x + 3
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. 2x + 6 x - 4 f(x) ==
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. f(x) = 4 - 3x 2x + 1
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. f(x) = -6 x + 9
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. 3 f(x) : х
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
Use the graph of the function to solve each equation or inequality.(a) ƒ(x) = 0 (b) ƒ(x) ≤ 0 y = f(x) -2 12 3 -6
Comprehensive graphs of four polynomial functions are shown in A–D. They represent the graphs of functions defined by these four equations, but not necessarily in the order listed.y = x3 - 3x2 - 6x
To perform the divisionusing synthetic division, we begin by writing the following. x 3)x + 6x + 2x -
Find a polynomial function ƒ of least degree having only real coefficients with zeros -2, 3, and 3 - i.
Solve each equation. 5х + 8 2х — 10 2х 10 -2
Comprehensive graphs of four polynomial functions are shown in A–D. They represent the graphs of functions defined by these four equations, but not necessarily in the order listed.y = x3 - 3x2 - 6x
Use synthetic division to perform each division. x3 + 7x2 + 13x + 6 x + 2
Match each equation in Column I with the description of the parabola that is its graph in Column II.y = -(x + 4)2 + 2A. Vertex (-2, 4), opens upB. Vertex (-2, 4), opens downC. Vertex (-4, 2), opens
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = -4x5 + 16x4 + 13x3 - 76x2 - 3x + 18
Solve each equation. x = 13VX – 40
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.x3 - 5x2 + 3x + 1; x - 1
Solve each problem.If m varies jointly as x and y, and m = 10 when x = 2 and y = 14, find m when x = 21 and y = 8.
Use synthetic division to perform each division. 5x4 + 5x³ + 2x2 – x – 3
Match each equation in Column I with the description of the parabola that is its graph in Column II.y = -(x + 2)2 + 4A. vertex (-2, 4), opens upB. vertex (-2, 4), opens downC. vertex (-4, 2), opens
Graph each rational function. Зх + 1 f(x) х2 + 7х + 10
Solve each equation. V2x – 5 – Vx – 3 = 1
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.x3 + 6x2 - 2x - 7; x + 1
Solve each problem.If m varies jointly as z and p, and m = 10 when z = 2 and p = 7.5, find m when z = 6 and p = 9.
Use synthetic division to perform each division. 2x4 — х3 — 7х? + 7х — 10 х — 2
Match each equation in Column I with the description of the parabola that is its graph in Column II.y = (x + 4)2 + 2A. vertex (-2, 4), opens upB. vertex (-2, 4), opens downC. vertex (-4, 2), opens
Graph each rational function. x2 + 2x + 1 f(x) =
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.2x4 + 5x3 - 8x2 + 3x + 13; x + 1
Solve each problem.If y varies inversely as x, and y = 10 when x = 3, find y when x = 20.
Use synthetic division to perform each division. x4 + 4x3 + 2x² + 9x + 4
Consider the graph of each quadratic function. Do the following.(a) Give the domain and range. (b) Give the coordinates of the vertex.(c) Give the equation of the axis. (d) Find the
Solve each equation. 3 x2/3 + 2 4
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. f(x) 5 4
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.-3x4 + x3 - 5x2 + 2x + 4; x - 1
Solve each problem.If y varies inversely as x, and y = 20 when x = 1/4, find y when x = 15.
Use synthetic division to perform each division. Зх + 9 x4 + 5x3 + 4x² x + 3
Graph each function. Determine the largest open intervals of the domain over which each function is (a) Increasing (b) Decreasing. f(x) 1 4 6 X
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing.ƒ(x) = 2x4
Comprehensive graphs of four polynomial functions are shown in A–D. They represent the graphs of functions defined by these four equations, but not necessarily in the order listed.y = x3 - 3x2 - 6x
Solve each problem.If y varies directly as x, and y = 9 when x = 30, find y when x = 40.
The product of a complex number and its conjugate is always a real number.Determine whether each statement is true or false. If false, explain why.
Solve each equation.(x - 5)-4 - 13(x - 5)-2 = -36
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = 2x4 - 9x3 - 5x2 + 57x - 45
Match each equation in Column I with the description of the parabola that is its graph in Column II.y = (x + 2)2 + 4A. vertex (-2, 4), opens upB. vertex (-2, 4), opens downC. vertex (-4, 2), opens
Use synthetic division to perform each division. 11x + 9 x3 + 3x2 + 9 x + 1
Comprehensive graphs of four polynomial functions are shown in A–D. They represent the graphs of functions defined by these four equations, but not necessarily in the order listed.y = x3 - 3x2 - 6x
Solve each problem.If y varies directly as x, and y = 20 when x = 4, find y when x = -6.
Solve each equation. + 0.25x = 1 =-x - Ex 2*
Graph each polynomial function. Factor first if the polynomial is not in factored form.ƒ(x) = x(x - 2)3(x + 2)2
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 graph of ƒ(x) = -2x2 - 6x + 5 opens down with y-intercept (0, ________), so it has x-intercept(s).
Consider the following function.By inspection, we can state that ƒ(2) = _______________. f(x) = 2x4 + 6x³ – 5x² + 3x + 8 f(x) = (x – 2)(2x³ + 10x² + 15x + 33) + 74
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
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
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
Fill in the blank(s) to correctly complete each sentence.The axis of symmetry of the graph of ƒ(x) = 2(x + 4)2 - 6 has equation x = _________.
To perform the divisionusing synthetic division, we begin by writing the following. 3 x + 2)x + 4x + 2
Comprehensive graphs of four polynomial functions are shown in A–D. They represent the graphs of functions defined by these four equations, but not necessarily in the order listed.y = x3 - 3x2 - 6x
Fill in the blank(s) to correctly complete each sentence, or answer the question as appropriate.In the equation y = 12/x, y varies inversely as x. When x = 3, y = 4. What is the value of y when x = 6?
Use the graph of the function to solve each equation or inequality.(a) ƒ(x) = 0 (b) ƒ(x) > 0 = f(x) х 5 10 -10 2.
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) = 2x4 + x3 - 3x + 4; k = 2
Fill in the blank(s) to correctly complete each sentence.The highest point on the graph of a parabola that opens down is the __________ of the parabola.
To perform the division in Exercise 2 using synthetic division, we begin by writing the following.Exercise 2 2 3 х+3 х — 1)х2 + 2х + 3 x2 — х Зх + 3 Зх — 3
Comprehensive graphs of four polynomial functions are shown in A–D. They represent the graphs of functions defined by these four equations, but not necessarily in the order listed.y = x3 - 3x2 - 6x
Fill in the blank(s) to correctly complete each sentence, or answer the question as appropriate.In the equation y = 6x, y varies directly as x. When x = 5, y = 30. What is the value of y when x = 10?
Use the graph of the function to solve each equation or inequality.(a) ƒ(x) < 0 (b) ƒ(x) > 0 -1 y = f(x) V
Fill in the blank(s) to correctly complete each sentence.The lowest point on the graph of a parabola that opens up is _________ the of the parabola.
Fill in the blank(s) to correctly complete each sentence, or answer the question as appropriate.For k > 0, if y varies inversely as x, then when x increases, y________, and when x decreases,

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