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College Algebra 7th Edition Robert F Blitzer - Solutions

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(x - 1)(x + 2)
Determine if f is odd, even, or neither. f(x) = 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(x + 1)²
Determine if f is odd, even, or neither. f(x) = -3x
Determine if f is odd, even, or neither. f(x) = 5x
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) = -xx - 2)7
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 76–83, use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). f(x) = √√/2 - x
In Exercises 67–80, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x)=√x + 2-2
In Exercises 76–81, find the domain of each function. g(x) = 4 x - 7
In Exercises 76–83, use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). f(x) X 2
In Exercises 76–81, find the domain of each function. h(x) = V8 - 2x
In Exercises 75–82, express the given function h as a composition of two functions f and g so that h(x) = (f ° g)(x). h(x) = √x²-9
In Exercises 67–80, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x) = √x + 1 − 1 Vx+1-1
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 75–82, express the given function h as a composition of two functions f and g so that h(x) = (f ° g)(x). h(x) = 2 √5x² + 3
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 76–81, find the domain of each function. f(x) X x² + 4x + 4x - 21
In Exercises 77–78, give the slope and y-intercept of each line whose equation is given. Assume that B ≠ 0.Ax = By - C
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 67–80, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = 2√x + 2 - 2
What is a circle? Without using variables, describe how the definition of a circle can be used to obtain a form of its equation.
In Exercises 85–86, finda. (f ° g)(x);b. (g ° f)(x);c. (f ° g)(3). f(x)=√x, g(x) = x + 1
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
Use the graphs of f and g to solve Exercises 83–90. y = g(x) HH y .y = f(x) # X
In Exercises 79–80, find the value of y if the line through the two given points is to have the indicated slope.(3, y) and (1, 4), m = -3
Give an example of a circle’s equation in standard form. Describe how to find the center and radius for this circle.
Use the figure to make the lists in Exercises 85–86.List the slopes m1 , m2 , m3 , and m4 in order of decreasing size. y y = m₁x + b₁ y = m₂x + b₂ X - y = m3x + b3 y = m4x + b4
In Exercises 84–86, use a graphing utility to graph f and g in the same [-8, 8, 1] by [-5, 5, 1] viewing rectangle. In addition, graph the line y = x and visually determine if f and g are inverses. f(x) 1 - X + 2, g(x) = 1 x - 2
Write and solve a problem about the flying time between a pair of cities shown on the cellphone screen for Exercises 71–72. Do not use the pairs in Exercise 71 or Exercise 72. Begin by determining a reasonable average speed, in miles per hour, for a jet flying between the cities.Data from
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 81–94, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. h(x) = x + 4 - 2
In Exercises 76–83, use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one).f(x) = int(x - 2)
Use the graphs of f and g to solve Exercises 83–90. Find (fg)(2). y = g(x) HH y .y = f(x) # X
In Exercises 81–82, graph each linear function.3x - 4f(x) - 6 = 0
In Exercises 76–83, use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one).f(x) =|x - 2|
In Exercises 83–85, use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. x² + 10x + y² - 4y - 20 = 0
In Exercises 81–94, begin by graphing the absolute value function, f(x) = |x| . Then use transformations of this graph to graph the given function. h(x) = x +31-2
In Exercises 87–88, finda. (f ° g)(x);b. the domain of (f ° g). f(x) x + 1 x - 2' g(x) = 1 X
In Exercises 76–83, use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one).f(x) = (x - 1)3
How is the standard form of a circle’s equation obtained from its general form?
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 84–86, use a graphing utility to graph f and g in the same [-8, 8, 1] by [-5, 5, 1] viewing rectangle. In addition, graph the line y = x and visually determine if f and g are inverses. f(x) = √x - 2, g(x) = (x + 2)³
In Exercises 85–86, finda. (f ° g)(x);b. (g ° f)(x);c. (f ° g)(3).f(x) = x2 + 3, g(x) = 4x - 1
Use the figure to make the lists in Exercises 85–86.List the y-intercepts b1 , b2 , b3 , and b4 in order of decreasing size. y y = m₁x + b₁ y = m₂x + b₂ X - y = m3x + b3 y = m4x + b4
Use the graphs of f and g to solve Exercises 83–90. Find the domain of f + g. y = g(x) HH y .y = f(x) # X
In Exercises 81–94, begin by graphing the absolute value function, f(x) = |x| . Then use transformations of this graph to graph the given function. h(x) = -x + 4|
In Exercises 86–89, determine whether each statement makes sense or does not make sense, and explain your reasoning.To avoid sign errors when finding h and k, I place parentheses around the numbers that follow the subtraction signs in a circle’s equation.
In Exercises 87–90, determine whether each statement makes sense or does not make sense, and explain your reasoning.I found the inverse of f(x) = 5x - 4 in my head: The reverse of multiplying by 5 and subtracting 4 is adding 4 and dividing by 5, so f -1(x) =x + 4/5.
In Exercises 86–89, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used the equation (x + 1)2 + (y - 5)2 = -4 to identify the circle’s center and radius.
In Exercises 75–82, express the given function h as a composition of two functions f and g so that h(x) = (f ° g)(x). h(x) = |3x - 4|
In Exercises 75–82, express the given function h as a composition of two functions f and g so that h(x) = (f ° g)(x). h(x) = 1 2x - 3
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 75–82, express the given function h as a composition of two functions f and g so that h(x) = (f ° g)(x). h(x) = |2x - 5]
In Exercises 79–80, find the value of y if the line through the two given points is to have the indicated slope. (-2, y) and (4,-4), m = 33
In Exercises 76–81, find the domain of each function. g(x): || Vx - 2 x - 5
In Exercises 67–80, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = 2√x + 1 - 1 21
In Exercises 75–82, express the given function h as a composition of two functions f and g so that h(x) = (f ° g)(x). h(x) 1 4x + 5
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 81–94, begin by graphing the absolute value function, f(x) = |x| . Then use transformations of this graph to graph the given function. + + |x| = (x)8
In Exercises 76–81, find the domain of each function. f(x) = √x −1+ √x + 5
Does (x - 3)2 + (y - 5)2 = -25 represent the equation of a circle? What sort of set is the graph of this equation?
In Exercises 81–82, graph each linear function.6x - 5f(x) - 20 = 0
In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function.f(x) = 3x - 1, g(x) = x - 5
In Exercises 76–83, use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). f(x) -V16 16x²
Use the graphs of f and g to solve Exercises 83–90. Find (f + g)(-3). y = g(x) HH y .y = f(x) # X
In Exercises 81–94, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. g(x) = x + 3
In Exercises 83–85, use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. x² + y² = 25
In Exercises 71–92, find and simplify the difference quotient f(x +h)-f(x) h -, h = 0
In Exercises 81–94, begin by graphing the absolute value function, f(x) = |x| . Then use transformations of this graph to graph the given function. g(x) = |x + 4|
In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function.f(x) = x2 + x + 1, g(x) = x2 - 1
If one point on a line is (3, -1) and the line’s slope is -2, find the y-intercept.
Use the graphs of f and g to solve Exercises 83–90. Find (g - f)(-2). y = g(x) HH y .y = f(x) # X
If one point on a line is (2, -6) and the line’s slope is - 3/2, find the y-intercept.
In Exercises 81–94, begin by graphing the absolute value function, f(x) = |x| . Then use transformations of this graph to graph the given function. g(x) = |x + 3|
In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x) = √x + 7, g(x) = √x - 2
In Exercises 84–86, use a graphing utility to graph f and g in the same [-8, 8, 1] by [-5, 5, 1] viewing rectangle. In addition, graph the line y = x and visually determine if f and g are inverses.f(x) = 4x + 4, g(x) = 0.25x - 1
List by letter all relations that are not functions.a. {(7, 5), (8, 5), (9, 5)}b. {(5, 7), (5, 8), (5, 9)}c.d. x2 + y2 = 100e. у - Х
In Exercises 16–23, let f(x) = x2 - x - 4 and g(x) = 2x - 6. Find f(x +h)-f(x) h
In Exercises 17–32, use the graph of y = f(x) to graph each function g.g(x) = f(x - 1) + 2 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
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.a.b.c. f(x) = 4x + 5
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.a.b.c.d. h(x) = x4 x² + 1
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.a.b.c. g(x) = x² 10x - 3
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.a.b.c. g(x) = x² + 2x + 3
we worked with data involving the increasing number of U.S. adults ages 18 and older living alone. The bar graph reinforces the fact that one-person households are growing more common. It shows one-person households as a percentage of the U.S. total for five selected years from 1980 through 2012.a.
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.a.b.c. f(x) = 3x + 7
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.a.b.c.d. h(x) = x³ = x + 1 -
In Exercises 33–34, find and simplify the difference quotientfor the given function.f(x) = 8x - 11 f(x + h) − f(x)¸ h ‡ 0 h
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Passing through (-3, 6) and (3, -2)
In Exercises 31–50, find f + g, f - g, fg, and f/g. Determine the domain for each function.f(x) = 3x - 4, g(x) = x + 2
If you know a point on a line and you know the equation of a line perpendicular to this line, explain how to write the line’s equation.
In Exercises 33–44, use the graph of y = f(x) to graph each function g.g(x) = f(x) + 2 -4,0) -5-4-3 4-33 y = f(x) y (0,0) 2- 3.4 45 -2) (4-2) X
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) = 3x2
In Exercises 33–36, use possible symmetry to determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd. ------ -2, y CI (0,4) 2 14 -4-3-2-1₁. 1 2 3 4 # ILIPOIII] X
Which graphs in Exercises 29–34 represent functions that have inverse functions? y X
In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius.Center (3, 2), r = 5
In Exercises 27–38, graph each equation in a rectangular coordinate system.f(x) = x2 - 4
In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Passing through (-3, -1) and (4, -1)
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.a.b.c. f(x) || 4x² 2 1

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