Question: Find the domain and range of each
Find the domain and range of each function. 
> Each graph is the graph of a polynomial function. Answer the following questions for each graph: (A) What is the minimum degree of a polynomial function that could have the graph? (B) Is the leading coefficient of the polynomial negative or positive?
> For each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercepts ((x) = (2x – 5)2 (x2 – 9)4
> Find the vertex form of each quadratic function by completing the square. ((x) = -5x2 + 15x - 11
> Find the vertex form of each quadratic function by completing the square. ((x) = 3x2 + 18x + 21
> Find the vertex form of each quadratic function by completing the square. ((x) = x2 - 12x - 8
> Find the vertex form of each quadratic function by completing the square. ((x) = x2 + 16x
> The table gives performance data for a boat powered by an Evinrude outboard motor. Find a quadratic regression model (y = ax2 + bx + c) for fuel consumption y (in miles per gallon) as a function of engine speed (in revolutions per minute). Estimate the f
> Refer to Problem 75. Find the distance from the center that the rate of flow is 30 centimeters per second. Round answer to two decimal places. Data from Problem 75: Find the distance from the center that the rate of flow is 20 centimeters per second. Ro
> Find the solution Set.
> Use the revenue function from Problem 70 and the given cost function: R(x) = x (2,000 - 60x) Revenue function C(x) = 4,000 + 500x Cost function where x is thousands of computers, and R(x) and C(x) are in thousands of dollars. Both functions have domai
> Use the revenue function from Problem 70, and the given cost function: R(x) = x(2,000 - 60x) Revenue function C(x) = 4,000 + 500x Cost function where x is thousands of computers, and C(x) and R(x) are in thousands of dollars. Both functions have do
> The marketing research department for a company that manufactures and sells notebook computers established the following price–demand and revenue functions: p(x) = 2,000 - 60x Price–demand function R(x) = xp(x) Revenue function = x (2,000 - 60x) where
> Using quadratic regression on a graphing calculator, show that the quadratic function that best fits the data on market share in Problem 66 is ((x) = -0.0117x2 + 0.32x + 17.9 Data from Problem 66:
> The table shows the retail market share of passenger cars from Ford Motor Company as a percentage of the U.S. market. A mathematical model for this data is given by ((x) = -0.0117x2 + 0.32x + 17.9 where x = 0 corresponds to 1980. (A) Complete the follo
> assume that a, b, c, h, and k are constants with a ( 0 such that ax2 + bx + c = a(x – h) 2 + k for all real numbers x. Show that:
> How can you tell from the vertex form y = a(x – h)2 + k whether a quadratic function has two real zeros?
> How can you tell from the standard form y = ax2 + bx + c whether a quadratic function has exactly one real zero?
> How can you tell from the graph of a quadratic function whether it has no real zeros?
> (A) Graph f and g in the same coordinate system. (B) Solve f1x2 = g1x2 algebraically to two decimal places. (C) Solve f1x2 7 g1x2 using parts (A) and (B). (D) Solve f1x2 6 g1x2 using parts (A) and (B). ((x)= -0.7x2 + 6.3x g(x) = 1.1x + 4.8 0 ( x (
> Find the slope and x intercept of the graph of each equation. 9x + 2y = 4
> Identify the graph(s) of lines with a positive slope.
> (A) Graph f and g in the same coordinate system. (B) Solve f1x2 = g1x2 algebraically to two decimal places. (C) Solve f1x2 7 g1x2 using parts (A) and (B). (D) Solve f1x2 6 g1x2 using parts (A) and (B). ((x) = -0.7x1x - 72 g(x) = 0.5x + 3.5 0 ( x (
> Given that f is a quadratic function with maximum ((x) = (( -3) = -5 , find the axis, vertex, range, and x intercepts.
> Solve graphically to two decimal places using a graphing calculator. 1.8x2 - 3.1x - 4.9 > 0
> Solve graphically to two decimal places using a graphing calculator 3.4 + 2.9x - 1.1x2 ( 0
> Solve graphically to two decimal places using a graphing calculator 7 + 3x - 2x2 = 0
> Use interval notation to write the solution set of the inequality x2 + 7x + 12 ( 0
> Use interval notation to write the solution set of the inequality (x + 6) (x – 3) < 0
> First write each function in vertex form; then find each of the following (to two decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range n(x) = -0.15x2 - 0.90x + 3.3
> First write each function in vertex form; then find each of the following (to two decimal places): (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range m(x) = 0.20x2 - 1.6x - 1
> Let ((x) = 100x - 7x2 - 10. Find the maximum value of ( to four decimal places graphically.
> Find the solution set
> Let g(x) = -0.6x2 + 3x + 4. Solve each equation graphically to two decimal places. (A) g(x) = -2 (B) g(x) = 5 (C) g(x) = 8
> Find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range V(x) = 0.5x2 + 4x + 10
> Find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range s(x) = -4x2 - 8x - 3
> Find the vertex form for each quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range g(x) = x2 - 6x + 5
> write an equation for each graph in the form y = a(x – h) 2 + k, where a is either 1 or -1 and h and k are integers.
> write an equation for each graph in the form y = a(x – h) 2 + k, where a is either 1 or -1 and h and k are integers.
> Find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range n(x) = (x – 4) 2 - 3
> Find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range g(x) = - (x + 2) 2 + 3
> Find each of the following to the nearest integer by referring to the graphs. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range Function g in the figure for Problem 14 Data from Problem 14:
> Find each of the following to the nearest integer by referring to the graphs. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range Function m in the figure for Problem 14 Data from Problem 14:
> Find the slope and x intercept of the graph of each equation. 3x + y = 6
> Match each equation with a graph of one of the functions f, g, m, or n in the figure. (A) y = (x – 3)2 - 4 (B) y = - (x + 3)2 + 4 (C) y = - (x – 3)2 + 4 (D) y = (x + 3)2 - 4
> write a brief verbal description of the relationship between the graph of the indicated function and the graph of y = x2 . n(x) = -x2 + 8x - 9
> write a brief verbal description of the relationship between the graph of the indicated function and the graph of y = x2 . g(x) = x2 - 2x - 5
> In This problem , graph each of the functions using the graphs of functions f and g below. y = g(x – 1)
> In This problem , graph each of the functions using the graphs of functions f and g below. y = g(x) - 1
> Find the domain and range of each function.
> Find the domain and range of each function.
> Find the domain and range of each function.
> Find the domain and range of each function.
> write the solution set using interval notation. -8 < -4x ( 12
> A production analyst has found that on average it takes a new person T(x) minutes to perform a particular assembly operation after x performances of the operation, where (A) Describe how the graph of function T can be obtained from the graph of one of t
> The average weight of a particular species of snake is given by w(x) = 463x3 , 0.2 ( x ( 0.8, where x is length in meters and w(x) is weight in grams. (A) Describe how the graph of function w can be obtained from the graph of one of the basic functions
> Table 6 shows state income tax rates for individuals filing a return in Louisiana. (A) Write a piecewise definition for T(x), the tax due on a taxable income of x dollars. (B) Graph T(x). (C) Find the tax due on a taxable income of $32,000. Of $64,000
> Table 4 shows the electricity rates charged by Monroe Utilities in the winter months. (A) Write a piecewise definition of the monthly charge w(x) for a customer who uses x kWh in a winter month. (B) Graph w(x).
> A company manufactures and sells in-line skates. Its financial department has established the price– demand function p1x2 = 190 - 0.0131x - 102 2 10 … x … 100 where p1x2 is the price at which x thousand pairs of in-line skates can be sold. (A) Describe h
> The manufacturer of the bicycle helmets is willing to supply x helmets at a price of p(x) as given by the equation p(x) = 4√x 9 ( x ( 289 (A) Describe how the graph of function p can be obtained from the graph of one of the basic funct
> Changing the order in a sequence of transformations may change the final result. Investigate each pair of transformations in this Problem to determine if reversing their order can produce a different result. Support your conclusions with specific example
> Changing the order in a sequence of transformations may change the final result. Investigate each pair of transformations in this Problem to determine if reversing their order can produce a different result. Support your conclusions with specific example
> Changing the order in a sequence of transformations may change the final result. Investigate each pair of transformations in this Problem to determine if reversing their order can produce a different result. Support your conclusions with specific example
> Graph involve a reflection in the x axis and/or a vertical stretch or shrink of one of the basic functions in Figure 1 on page 58. Identify the basic function, and describe the transformation verbally. Write an equation for the given graph. Figure-1:
> Find the slope and x intercept of the graph of each equation. y = -4x + 12
> Graph involve a reflection in the x axis and/or a vertical stretch or shrink of one of the basic functions in Figure 1 on page 58. Identify the basic function, and describe the transformation verbally. Write an equation for the given graph. Figure-1:
> Graph involve a reflection in the x axis and/or a vertical stretch or shrink of one of the basic functions in Figure 1 on page 58. Identify the basic function, and describe the transformation verbally. Write an equation for the given graph. Figure-1:
> Graph each function.
> Graph each function.
> Graph each function.
> The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using -5 ( x ( 5 and -5 ( y ( 5. The graph of ƒ(x)= x2 is reflected in the x axis and shi
> The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using -5 ( x ( 5 and -5 ( y ( 5. The graph of ƒ(x)= | x | is reflected in the x axis and
> The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and graph g using -5 ( x ( 5 and -5 ( y ( 5.
> Graph in this Problem is the result of applying a sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given gra
> Graph in this Problem is the result of applying a sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given gra
> write the solution set using interval notation 3x ( 12
> Graph in this Problem is the result of applying a sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given gra
> Graph in this Problem is the result of applying a sequence of transformations to the graph of one of the six basic functions in Figure 1 on page 58. Identify the basic function and describe the transformation verbally. Write an equation for the given gra
> Describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. m(x) = –0.4x2 is
> Describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. /
> Describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. m(x) = (x + 3)2 + 4
> Describe how the graph of each function is related to the graph of one of the six basic functions in Figure 1 on page 58. Sketch a graph of each function. h (x) = - | x - 5 |
> In This problem , graph each of the functions using the graphs of functions f and g below. y = - (0.5g (x) + 3
> In This problem , graph each of the functions using the graphs of functions f and g below. y = -0.5g (x) + 3
> In This problem , graph each of the functions using the graphs of functions f and g below. y = 2 ((x)
> In This problem , graph each of the functions using the graphs of functions f and g below. y = -g (x)
> Find the slope and y intercept of the graph of each equation.
> In This problem , graph each of the functions using the graphs of functions f and g below. y = ((x) + 3
> In This problem , graph each of the functions using the graphs of functions f and g below. y = ( (x + 3)
> Indicate whether table specifies a function.
> Use point-by-point plotting to sketch the graph of each equation. xy = 12
> Use point-by-point plotting to sketch the graph of each equation. x = y3
> Use point-by-point plotting to sketch the graph of each equation. y = x2
> Use point-by-point plotting to sketch the graph of each equation. x = y + 1
> The percentage s of seats in the House of Representatives won by Democrats and the percentage v of votes cast for Democrats (when expressed as decimal fractions) are related by the equation 5v - 2s = 1.4 0 < s < 1, 0.28 < v < 0.68 (A) Express v a
> The financial department for the company in Problems 86 and 88 established the following cost function for producing and selling x thousand notebook computers: C1x2 = 4,000 + 500x thousand dollars (A) Write a profit function for producing and selling x
> (A) Using the price–demand function P(x) = 2,000 - 60x 1 ( x ( 25 from Problem 86, write the company’s revenue function and indicate its domain. (B) Complete Table 11, computing revenues to the nearest thousand
> write the solution set using interval notation -1 ( x < 5
> A company manufactures notebook computers. Its marketing research department, using statistical techniques, collected the data shown in Table 9, where p is the wholesale price per computer at which x thousand computers can be sold. Using special analytic
> Refer to the area A and perimeter P of a rectangle with length l and width w (see the figure). The perimeter of a rectangle is 160 m. Express the area A1w2 as a function of the width w, and state the domain of this function.
> Refer to the area A and perimeter P of a rectangle with length l and width w (see the figure). The area of a rectangle is 81 sq in. Express the perimeter P1l2 as a function of the length l, and state the domain of this function
