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College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions

In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line.y = 2/5x - 1
In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. (x + 2)² + (y + 2)² = 4
Solve: 2x2/3 - 5x1/3 - 3 = 0.
In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = x³, g(x) = x³ - 1
In Exercises 45–52, use the graph of y = f(x) to graph each function g.g(x) = -f(x - 1) + 1 y = f(x) (-2,0) -5-4-3-2- y TI (0, 2) (2, 2) (4,0) 2 3 4 5 (-4,-2) |||| [III]?|IIIID X
In Exercises 31–50, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x)=√x + 4, g(x) = √x - 1
In Exercises 37–48, determine whether each function is even, odd, or neither. Then determine whether the function’s graph is symmetric with respect to the y-axis, the origin, or neither. f(x)=x√1-x²
Exercises 47–49 will help you prepare for the material covered in the next section. In each exercise, graph the functions in parts (a) and (b) in the same rectangular coordinate system.a. Graph f(x) = |x| using the ordered pairs (-3, f(-3)), (-2, f(-2)), (-1, f( -1)), (0, f(0)), (1, f(1)), (2,
In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line.f(x) = -4x + 5
In Exercises 39–52,a. Find an equation for f -1(x).b. Graph f and f -1 in the same rectangular coordinate system.c. Use interval notation to give the domain and the range of f and f -1.f(x) = (x + 2)3
In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. g(x) = 1 2 X
Find the average rate of change of f(x) = 3x2 - x from x1 = -1 to x2 = 2.
In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. (x + 4) + (y + 5)² = 36
In Exercises 45–52, use the graph of y = f(x) to graph each function g.g(x) = -f(x + 1) - 1 y = f(x) (-2,0) -5-4-3-2- y TI (0, 2) (2, 2) (4,0) 2 3 4 5 (-4,-2) |||| [III]?|IIIID X
In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = 3, g(x) = 5
In Exercises 31–50, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x)=√x + 6, g(x) = √x - 3
In Exercises 39–52,a. Find an equation for f -1(x).b. Graph f and f -1 in the same rectangular coordinate system.c. Use interval notation to give the domain and the range of f and f -1.For Exercises 49–52: To solve for a variable involving an nth root, raise both sides of the equation to the
Exercises 47–49 will help you prepare for the material covered in the next section. In each exercise, graph the functions in parts (a) and (b) in the same rectangular coordinate system.a. Graph f(x) = x2 using the ordered pairs (-3, f(-3)), (-2, f(-2)), (-1, f(-1)), (0, f(0)), (1, f(1)), (2,
In Exercises 37–48, determine whether each function is even, odd, or neither. Then determine whether the function’s graph is symmetric with respect to the y-axis, the origin, or neither. f(x) = x²√₁-x²
In Exercises 39–52,a. Find an equation for f -1(x).b. Graph f and f -1 in the same rectangular coordinate system.c. Use interval notation to give the domain and the range of f and f -1.f(x) = (x - 2)3
In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. g(x) = 1 -X 3
In Exercises 39–52,a. Find an equation for f -1(x).b. Graph f and f -1 in the same rectangular coordinate system.c. Use interval notation to give the domain and the range of f and f -1. For Exercises 49–52: To solve for a variable involving an nth root, raise both sides of the equation to the
In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line.2x + 3y + 6 = 0
In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. x² + (y − 1)² = 1
In Exercises 45–52, use the graph of y = f(x) to graph each function g.g(x) = 2f(1/2x) y = f(x) (-2,0) -5-4-3-2- y TI (0, 2) (2, 2) (4,0) 2 3 4 5 (-4,-2) |||| [III]?|IIIID X
In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = -1, g(x) = 4
Exercises 47–49 will help you prepare for the material covered in the next section. In each exercise, graph the functions in parts (a) and (b) in the same rectangular coordinate system.a. Graph f(x) = x3 using the ordered pairs (-2, f(-2)), (-1, f(-1)), (0, f(0)), (1, f(1)), and (2, f(2)).b.
In Exercises 31–50, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x) = √x - 2, g(x) = V2-x
In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line.2y - 8 = 0
In Exercises 31–50, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x)=√x-5, g(x) = √5 - x
In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. x² + (y-2)² = 4
In Exercises 45–52, use the graph of y = f(x) to graph each function g.g(x) = 1/2 f(2x) y = f(x) (-2,0) -5-4-3-2- y TI (0, 2) (2, 2) (4,0) 2 3 4 5 (-4,-2) |||| [III]?|IIIID X
In Exercises 51–54, graph the given square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph
In Exercises 49–58, graph each equation in a rectangular coordinate system.y = -2
Graph using intercepts: 2x - 5y - 10 = 0.
In Exercises 49–58, graph each equation in a rectangular coordinate system.y = 4
In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. (x + 1)² + y² = 25
In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²4x12y9 = 0
In Exercises 53–58, evaluate each piecewise function at the given values of the independent variable. h(x) a. h(5) X² - 9 x - 3 6 if x # 3 x = 3 if b. h(0) c. h(3)
In Exercises 53–58, evaluate each piecewise function at the given values of the independent variable. g(x) a. g(0) (x + 5 if x = -5 -(x + 5) if x < -5 b. g(-6) c. g(-5)
In Exercises 55–59, use the graph of y = f(x) to graph each function g.g(x) = -f(2x) -4-3 N W 2- 1+ 2+ 2/3 4 y = f(x) X
In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. (g ° f )(0) X -1 0 1 2 f(x) 1 4 5 -1 X -1 1 4 10 g(x) 0 1 2 -1
In Exercises 53–66, begin by graphing the standard quadratic function, f(x) = x2. Then use transformations of this graph to graph the given function. h(x) = (x - 2)²
In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² + 8x - 2y = 8 = 0
In Exercises 55–64, use the vertical line test to identify graphs in which y is a function of x. y X
In Exercises 49–58, graph each equation in a rectangular coordinate system.f(x) = 3
In Exercises 55–59, use the graph of y = f(x) to graph each function g.g(x) = 2f(1/2x) -4-3 N W 2- 1+ 2+ 2/3 4 y = f(x) X
In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. f -1(g(10)) X -1 0 1 2 f(x) 1 4 5 -1 X -1 1 4 10 g(x) 0 1 2 -1
In Exercises 53–58, evaluate each piecewise function at the given values of the independent variable. h(x) a. h(7) x² - 25 x-5 10 if x # 5 if x = 5 b. h(0) c. h(5)
In Exercises 55–64, use the vertical line test to identify graphs in which y is a function of x. y X
In Exercises 53–66, begin by graphing the standard quadratic function, f(x) = x2. Then use transformations of this graph to graph the given function. 2 h(x) = (x - 1)²
In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y2 + 12x - бу - 4 = 0
In Exercises 49–58, graph each equation in a rectangular coordinate system.3x - 18 = 0
In Exercises 55–59, use the graph of y = f(x) to graph each function g.g(x) = -f(-x) - 1 -4-3 N W 2- 1+ 2+ 2/3 4 y = f(x) X
In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. f -1(g(1)) X -1 0 1 2 f(x) 1 4 5 -1 X -1 1 4 10 g(x) 0 1 2 -1
In Exercises 53–66, begin by graphing the standard quadratic function, f(x) = x2. Then use transformations of this graph to graph the given function. h(x) = (x - 2)² + 1
In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² - 2x + y² - 15 = 0
In Exercises 59–70, the domain of each piecewise function is (- ∞, ∞).a. Graph each function.b. Use your graph to determine the function’s range. f(x) = -X X if x < 0 if x ≥ 0
In Exercises 55–64, use the vertical line test to identify graphs in which y is a function of x. У X
In Exercises 49–58, graph each equation in a rectangular coordinate system.3x + 12 = 0
In Exercises 59–66,a. Rewrite the given equation in slope-intercept form.b. Give the slope and y-intercept.c. Use the slope and y-intercept to graph the linear function. 3x + y - 5 = 0 :
In Exercises 59–64, let Evaluate the indicated function without finding an equation for the function.(f ° g)(0) f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2.
In Exercises 53–66, begin by graphing the standard quadratic function, f(x) = x2. Then use transformations of this graph to graph the given function. h(x) = (x - 1) + 2
In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x2 + y² — бу — 7 = 0
In Exercises 55–64, use the vertical line test to identify graphs in which y is a function of x. y x=
In Exercises 59–70, the domain of each piecewise function is (- ∞, ∞).a. Graph each function.b. Use your graph to determine the function’s range. f(x) = -X if if x ≥ 0 x < 0 >
In Exercises 59–64, let Evaluate the indicated function without finding an equation for the function.(g ° f)(0) f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2.
Simplify the powers of ii32
A cylindrical tank contains 500 galIons of water. A plug is pulled from the bottom of the tank, and it takes 10 minutes to drain the tank. The amount A of water in gallons remaining in the tank after 1 minutes is approximated by(a) What is a reasonable domain for A? (b) Evaluate 4(1) and interpret
A runner is working out on a straight track. The graph shows the runner's distance y in hundreds of feet from the starting line after 1 minutes. (a) Estimate the turning points. (b) Interpret each turning point. Start Distance (feet X 100) 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 01 123 Time (minutes) 5
Determine if the function is a polynomial function. If it is, state its degree and leading coefficient a. f(x) = 2x³ = x + 5
Divide the expression. 5x4 - 15 10x
Use the graph off to complete the following.(a) Determine where f is increasing or decreasing. (b) Identify any local extrema. (c) Identify any absolute extrema. (d) Approximate the x-coordinates of the x-intercepts and zeros of f. Then solve f(x) = 0. How are the x-coordinates of the
Use transformations to sketch a graph of f. I + x^= (x)/
Continuing with Exercise 101, make a conjecture about which viewing rectangles result in the graph of a circle with radius 5 and center at the origin appearing circular. i. [-9,9,1] by [-6, 6, 1] ii. [-5, 5, 1] by [-10, 10, 1] iii. [5, 5, 1] by [-5, 5, 1] iv. [-18, 18, 1] by
Use the accompanying graph of y = f(x) to sketch a graph of each equation. (a) y = f(x - 1) - 2 (b) y = −f(x) + 1 () y = f(x) -3-2 3 2 ㅜㅜㅜ y=f(x) 23
Use the graph shown to sketch a graph of each equation. y=f(x)
Predict how the graph of each equation will appear compared to the graph of f(x) = x2. (a) y = (x + 4)² (c) y = (x - 5)² + 3 (b) y=x²-3
Use the table for f(x) to make tables for g(x) and h(x). (a) g(x) = f(x-2) + 3 (b) h(x) = -2f(x + 1)
Write an equation that transforms the graph of f(x) = x2 in the desired ways. Do not simplify. (a) Right 3 units, downward 4 units (b) Reflected about the x-axis (c) Shifted left 6 units, reflected about the y-axis (d) Reflected about the y-axis, shifted left 6 units
Write the equation of the graph. (The given graph is a translation of the graph of one of the following equations: y = x2, y = √x, or y = |x|.) -3 -1
Use the graph to find the following. (a) Sign of the leading coefficient (b) Vertex (c) Axis of symmetry (d) Intervals where f is increasing and where f is decreasing y = f(x) -3 3 2 1 12
Write the equation of the graph. (The given graph is a translation of the graph of one of the following equations: y = x2, y = √x, or y = |x|.) -1 y 1 2 3 4 5
Use the graph to find the following. (a) Sign of the leading coefficient (b) Vertex (c) Axis of symmetry (d) Intervals where f is increasing and where f is decreasing 432 123 -y=f(x).
Write f(x) in the general form f(x) = ax2 + bx+c, and identify the leading coefficient. f(x) = (x + 1)² - 2
Write f(x) in the general form f(x) = ax2 + bx+c, and identify the leading coefficient. f(x) = -2(x - 5)² + 1
Use transformations to sketch a graph of the equation y = √x + 1-2
Write the equation of the graph. (The given graph is a translation of the graph of one of the following equations: y = x2, y = √x, or y = |x|.) -5 -3 2
Write the equation of the graph. (The given graph is a translation of the graph of one of the following equations: y = x2, y = √x, or y = |x|.) 3 2 I 123
Write the equation of the graph. (The given graph is a translation of the graph of one of the following equations: y = x2, y = √x, or y = |x|.) 5 3 2 1234 X
Use the graph of the quadratic function f to write it as f(x) = a(x - h)2 + k. y = f(x) 1 2 3
Write f(x) in the vertex form f(x) = a(x - h)2 + k, and identify the vertex. [ = x9 + ₂x = (x)f
Write the equation of the graph. (The given graph is a translation of the graph of one of the following equations: y = x2, y = √x, or y = |x|.) -1 3 2 1 12
Use the graph of the quadratic function f to write it as f(x) = a(x - h)2 + k. y = f(x) 24 ➤X
Write f(x) in the vertex form f(x) = a(x - h)2 + k, and identify the vertex. f(x) = 2x² + 4x −- 5
Write the equation of the graph. (The given graph is a translation of the graph of one of the following equations: y = x2, y = √x, or y = |x|.) 1 23
Suppose that h and k are positive numbers. Match each equation to its graph (a-d). y = (x + h)² - k
Suppose that h and k are positive numbers. Match each equation to its graph (a-d). y = √x + h-k
Suppose that h and k are positive numbers. Match each equation to its graph (a-d). y = (xh)² + k
Use the vertex formula to determine the vertex on the graph of f. f(x) = x² + 8x - 5

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