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College Algebra 7th Edition Robert F Blitzer - Solutions

If the domain of f(x) is given by [-2,4], what is the domain of |f(x)|?
If f(k) = -6, what is the value of |f(k)|?
If the domain of f(x) is given by (-∞, 0], what is the domain of |f(x)|?
If the range of f(x) is given by (-∞, 0], what is the range of |f(x)|?
If f(k) = 17, what is the value of |f(k)|?
In Exercises 17–32, determine whether the graph of each equation is symmetric with respect to the y-axis, the x-axis, the origin, more than one of these, or none of these. 2 x = y² + 6
In Exercises 17–32, use the graph of y = f(x) to graph each function g.g(x) = f(x - 1) T 321 4,0) 5-4-3-2-1 3- y IIII] y = f(x) 8:00:07 11 (2,2) 2 (0, 0) (4,0) 2 3 4 5 (-2,-2) 3- [IIIII|IIIII X
The functions in Exercises 11–28 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.f(x) = (x + 2)3
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.For what value or values of x is f(x) = -2? y = f(x) # [TD y X
In Exercises 11–26, determine whether each equation defines y as a function of x. 4x = y² 2
In Exercises 1–30, find the domain of each function. f(x)=√x + 2
In Exercises 19–24, write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions.The graph of f passes through (-1, 5) and is perpendicular to the line whose equation is x = 6.
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Slope = -2, passing through (0, -3)
In Exercises 17–32, determine whether the graph of each equation is symmetric with respect to the y-axis, the x-axis, the origin, more than one of these, or none of these. y = x² + 6
In Exercises 17–32, use the graph of y = f(x) to graph each function g.g(x) = f(x) - 1 T 321 4,0) 5-4-3-2-1 3- y IIII] y = f(x) 8:00:07 11 (2,2) 2 (0, 0) (4,0) 2 3 4 5 (-2,-2) 3- [IIIII|IIIII X
The functions in Exercises 11–28 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.f(x) = x3 + 2
In Exercises 1–30, find the domain of each function. f(x)=√x - 3
In Exercises 11–26, determine whether each equation defines y as a function of x. = y² x = X
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Slope = -4, passing through (-4, 0)
In Exercises 13–18, find the average rate of change of the function from x1 to x2. f(x)=√x from x₁ = 9 to x2 x1 = 16
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.Find f(-4). y = f(x) # [TD y X
In Exercises 17–32, determine whether the graph of each equation is symmetric with respect to the y-axis, the x-axis, the origin, more than one of these, or none of these. y = x² - 2
The functions in Exercises 11–28 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.f(x) = x3 - 1
In Exercises 17–32, use the graph of y = f(x) to graph each function g.g(x) = f(x) + 1 T 321 4,0) 5-4-3-2-1 3- y IIII] y = f(x) 8:00:07 11 (2,2) 2 (0, 0) (4,0) 2 3 4 5 (-2,-2) 3- [IIIII|IIIII X
Fill in each blank so that the resulting statement is true. If f(g(x)) = 3/g(x) - 4 and g(x) = 8/x, then 0 and________ must be excluded from the domain of f ° g.
In Exercises 13–18, find the average rate of change of the function from x1 to x2. f(x)=√x from x₁ = 4 to x₂ = 9
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.What is the relative maximum of f? y = f(x) # [TD y X
In Exercises 11–26, determine whether each equation defines y as a function of x. x² + y² = 25
In Exercises 1–30, find the domain of each function. f(x) = 1 4 x - 2 3
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = -f(2x) - 1 y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. (2V3, V6) and (-V3,5V6)
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Slope = -5, passing through (-4, -2)
The functions in Exercises 11–28 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.f(x) = 3x - 1
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.At what number does f have a relative maximum? y = f(x) # [TD y X
In Exercises 13–16, the graph of a function f is given. Use the graph to find each of the following:a. The numbers, if any, at which f has a relative maximum. What are these relative maxima?b. The numbers, if any, at which f has a relative minimum. What are these relative minima? f(x) =
In Exercises 13–18, find the average rate of change of the function from x1 to x2. f(x)=x²- 2x from x₁ = 3 to x₂ = 6
In Exercises 11–26, determine whether each equation defines y as a function of x. x² + y² = 16
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Slope = -3, passing through (-2, -3)
Fill in each blank so that the resulting statement is true.True or false: f(g(x)) = f(x) . g(x)_______ .
In Exercises 1–30, find the domain of each function. f(x) = 1 4 x - 1 - 2
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = -f(1/2x) + 1 y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. (3√3, √5) and (-√3,4√5)
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.Find the interval(s) on which f is decreasing. y = f(x) # [TD y X
The functions in Exercises 11–28 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.f(x) = 2x + 3
In Exercises 11–26, determine whether each equation defines y as a function of x.
In Exercises 13–18, find the average rate of change of the function from x1 to x2. f(x) = x² + 2x from x₁ 3 to x₂ = 5
In Exercises 13–16, the graph of a function f is given. Use the graph to find each of the following:a. The numbers, if any, at which f has a relative maximum. What are these relative maxima?b. The numbers, if any, at which f has a relative minimum. What are these relative minima? f(x) = 2x³ +
Fill in each blank so that the resulting statement is true.True or false: f ° g is the same function as g ° f ._________ .
In Exercises 11–26, determine whether each equation defines y as a function of x. x² + y = 25
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = f(2x) y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
In Exercises 13–18, find the average rate of change of the function from x1 to x2. f(x) 6x from x₁ 0 to x₂ = 4 X2
In Exercises 13–16, the graph of a function f is given. Use the graph to find each of the following:a. The numbers, if any, at which f has a relative maximum. What are these relative maxima?b. The numbers, if any, at which f has a relative minimum. What are these relative minima?
Fill in each blank so that the resulting statement is true.I find (g ° f)(x) by replacing each occurrence of x in the equation for_______ with_________.
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.Find the interval(s) on which f is increasing. y = f(x) # [TD y X
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. (0, -√2) and (√7,0)
The functions in Exercises 11–28 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.f(x) = 4x
In Exercises 1–30, find the domain of each function. h(x) = 4 X 5 - 1
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Slope = 8, passing through (4, -1)
In Exercises 1–30, find the domain of each function. h(x) = 3 X 4 1
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Slope = 6, passing through (-2, 5)
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = f(1/2x) y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. (0, -√3) and (√5,0)
The functions in Exercises 11–28 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.f(x) = 2x
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.Find the y-intercept. y = f(x) # [TD y X
In Exercises 13–18, find the average rate of change of the function from x1 to x2. f(x) = 3x from x₁ 0 to x₂ = 5
In Exercises 13–16, the graph of a function f is given. Use the graph to find each of the following:a. The numbers, if any, at which f has a relative maximum. What are these relative maxima?b. The numbers, if any, at which f has a relative minimum. What are these relative minima?
In Exercises 11–26, determine whether each equation defines y as a function of x. x + y = 25
In Exercises 1–30, find the domain of each function. g(x) 1 x² + 4 1 x² - 4 X
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = 2f(x) y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Slope = 4, passing through (1, 3)
Fill in each blank so that the resulting statement is true.The notation g ° f , called the________ of the function g with f , is defined by (g ° f )(x) =___________ .
In Exercises 11–26, determine whether each equation defines y as a function of x. x + y = 16
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.Find the x-intercept(s). y = f(x) # [TD y X
In Exercises 1–12, use the graph to determinea. Intervals on which the function is increasing, if any.b. Intervals on which the function is decreasing, if any.c. Intervals on which the function is constant, if any. +-+-+ y 2- -5-4-3-2-11 2.3 CIIIII|III] X
The functions in Exercises 11–28 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.f(x) = x + 5
Fill in each blank so that the resulting statement is true.The equation Ax + By + C = 0, where A and B are not both zero, is called the_________ form of the equation of a line.
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.(2.6, 1.3) and (1.6, -5.7)
In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general formPassing through (5, -9) and perpendicular to the line whose equation is x + 7y - 12 = 0
Fill in each blank so that the resulting statement is true.I find (f ° g)(x) by replacing each occurrence of x in the equation for_______ with________ .
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Slope = 2, passing through (3, 5)
Fill in each blank so that the resulting statement is true. If the x-intercepts of a function are -1 and 3, then f(-1) =_____ and f(3) =_____ . The x-intercepts, -1 and 3, are called the_____ of the function.
In Exercises 1–30, find the domain of each function. g(x) 1 x² + 1 1 x2-1
The functions in Exercises 11–28 are all one-to-one. For each function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.f(x) = x + 3
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = 1/2 f(x) y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.(3.5, 8.2) and (-0.5, 6.2)
Fill in each blank so that the resulting statement is true.The graph of the equation x = -2 is a/an__________ line.
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.Find the range of f. y = f(x) # [TD y X
In Exercises 1–12, use the graph to determinea. Intervals on which the function is increasing, if any.b. Intervals on which the function is decreasing, if any.c. Intervals on which the function is constant, if any. --3- --2- -3-2-1 y 2- ta ....... 2 3 4 5 X
In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general formPassing through (4, -7) and perpendicular to the line whose equation is x - 2y - 3 = 0
In Exercises 1–10, determine whether each relation is a function.Give the domain and range for each relation. {(4, 1), (5, 1), (6, 1)}
Fill in each blank so that the resulting statement is true.The notation f ° g, called the________ of the function f with g, is defined by (f ° g)(x) =_________.
Fill in each blank so that the resulting statement is true.The expressionis called the_________ of the function f. We find this expression by replacing x with________ each time x appears in the function’s equation. Then we subtract_______ . After simplifying, we factor_______ from the numerator
In Exercises 1–10, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (3,-4) and (3,5)
The shaded set of numbers shown on the y-axis can be expressed in interval notation as_______ . This set represents the function’s_______ . -3-2- H NWA 3 70 y = f(x) 1 2 3 THB X
In Exercises 1–30, find the domain of each function. f(x) = 1 x + 8 + 3 x - 10
In Exercises 1–10, find f(g(x)) and g( f(x)) and determine whether each pair of functions f and g are inverses of each other. f(x)=√x - 4 and g(x) = x³ + 4
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = f(-x) + 3 y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.Find the domain of f. y = f(x) # [TD y X
In Exercises 1–12, use the graph to determinea. Intervals on which the function is increasing, if any.b. Intervals on which the function is decreasing, if any.c. Intervals on which the function is constant, if any. y 1003 8 4.5 (IIHIIII] X
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.(0, -2) and (4, 3)

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