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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

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
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)
Fill in each blank so that the resulting statement is true.The graph of the equation y = 3 is a/an__________ line.
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
In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general formPassing through (-1, 3) and parallel to the line whose equation is 3x - 2y - 5 = 0
In Exercises 1–10, determine whether each relation is a function.Give the domain and range for each relation. {(1, 4), (1,5), (1, 6)}
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): 2 x - 5 and g(x) NIX 2 X + 5
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = -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 7–8, determine whether each equation defines y as a function of x.x + y2 = 5
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.(-4, -1) and (2, -3)
In Exercises 1–30, find the domain of each function. g(x) = 2 2 x² + x - 12
Fill in each blank so that the resulting statement is true.The slope-intercept form of the equation of a line is________ , where m represents the_______ and b represents the_________ .
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
In Exercises 1–10, determine whether each relation is a function.Give the domain and range for each relation. {(-7, -7), (-5, -5), (-3, -3), (0, 0)}
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
Fill in each blank so that the resulting statement is true.If any vertical line intersects a graph________ , the graph does not define y as a/an________ of x.
In Exercises 5–8, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Passing through (-4, 2) and perpendicular to the line whose equation is y
In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general formPassing through (-2, 2) and parallel to the line whose equation is 2x - 3y - 7 = 0
Fill in each blank so that the resulting statement is true.A function defined by two or more equations over a specified domain is called a/an__________ function.
Fill in each blank so that the resulting statement is true.The domain of g(x) =3/x - 2 consists of all real numbers except 2, represented in interval notation as (-∞, 2) ∪ ______ .
In Exercises 1–30, find the domain of each function. f(x) 1 x + 7 + 3 x-9
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
Fill in each blank so that the resulting statement is true.The domain of h(x) =1/x + 7/x - 3 consists of all real numbers except 0 and 3, represented in interval notation as (-∞, 0) ∪ _______ ∪
Fill in each blank so that the resulting statement is true. The greatest integer function is defined by int(x) = the greatest integer that is__________ . For example, int(2.5) =_______ , int(-2.5)
Fill in each blank so that the resulting statement is true.The shaded set of numbers shown on the x-axis can be expressed in interval notation as_______ . This set represents the function’s_______
Use the graph of f to solve Exercises 9–24. Where applicable, use interval notation.Explain why f represents the graph of a function. y = f(x) # [TD y X
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 and g(x) = -X
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
Fill in each blank so that the resulting statement is true.In order to graph the line whose equation is begin by plotting the point_________ . From this point, we move_______ units up (the rise)
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 (4, 1)
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
In Exercises 1–10, determine whether each relation is a function.Give the domain and range for each relation. {(10, 4), (-2,4), (-1, 1), (5, 6)}
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) = 3 x - 4 and g(x) || 3 X +4
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = 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 1–12, 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
In Exercises 1–30, find the domain of each function. g(x) = + 2 3 - 2x 15 -
Fill in each blank so that the resulting statement is true.If f(x) = x2 - 5x + 4, we can find f(x + 6) by replacing each occurrence of_______ by_______ .
Fill in each blank so that the resulting statement is true.If (x1, f(x1)) and (x2, f(x2)) are distinct points on the graph of a function f, the average rate of change of f from x1 to x2 is________ .
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
In Exercises 5–8, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Passing through (-2, -7) and parallel to the line whose equation is y =
Fill in each blank so that the resulting statement is true.f/g (x) =_______ . provided_________ ≠ 0
In Exercises 7–8, determine whether each equation defines y as a function of x.x2 + y = 5
Fill in each blank so that the resulting statement is true.The graph of y = f(1/5x) is obtained by a/an_______ stretch of the graph of y = f(x) by multiplying each of its_______ -coordinates by 5.
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) and (3, -4)
In Exercises 1–10, determine whether each relation is a function.Give the domain and range for each relation. {(-3, -3), (-2,-2), (-1, -1), (0, 0)}
Fill in each blank so that the resulting statement is true.The point-slope form of the equation of a nonvertical line with slope m that passes through the point (x1, y1) is_________ .
Fill in each blank so that the resulting statement is true. The graph of a function is the graph of its________ .
Fill in each blank so that the resulting statement is true. If f is an odd function, then f(-x) =______ . The graph of an odd function is symmetric with respect to the_______ .
In Exercises 5–8, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Passing through (2, -3) and perpendicular to the line whose equation is y
Fill in each blank so that the resulting statement is true.The domain of f(x) = 5x + 7 consists of all real numbers, represented in interval notation as_________ .
Fill in each blank so that the resulting statement is true.True or false: The graph of g(x) = √x + 4 is the graph of f(x) = √x shifted horizontally to the right by 4 units________.
Fill in each blank so that the resulting statement is true.If f is an even function, then f(-x) =_______ . The graph of an even function is symmetric with respect to the_______ .
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) = 3x - 7 and g(x) = x + 3 7
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, 0) and (3, -4)
In Exercises 1–6, determine whether each relation is a function. Give the domain and range for each relation. NA y --2- ************ X ============
Fill in each blank so that the resulting statement is true.In the equation (x2 + 4x ) + (y2 - 8y ) = 5, we complete the square on x by adding________ to both sides. We complete the square on y
In Exercises 5–8, use the given conditions to write an equation for each line in point-slope form and slope-intercept form.Passing through (-8, -10) and parallel to the line whose equation is y =
In Exercises 1–10, determine whether each relation is a function.Give the domain and range for each relation. {(3,-2), (5,-2), (7, 1), (4,9)}
Fill in each blank so that the resulting statement is true.The graph of y = 5f(x) is obtained by a/an________ stretch of the graph of y = f(x) by multiplying each of its_______ -coordinates by 5.
Fill in each blank so that the resulting statement is true.The slope of the line through the distinct points (x1, y1) and (x2, y2) can be interpreted as the rate of change in______ with respect
In Exercises 1–30, find the domain of each function. f(x) = x² + x - 12
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = f(x + 1) + 2 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 1–10, 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
Fill in each blank so that the resulting statement is true.(fg)(x) = _______ .
Fill in each blank so that the resulting statement is true.The graph of an equation is symmetric with respect to the________ if substituting -x for x and -y for y in the equation results in an
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
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) = 5x9 and g(x) = x + 5 9
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = f(x - 1) - 2 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, 0) and (-3, 4)
Fill in each blank so that the resulting statement is true.The slope of a horizontal line is________ .
In Exercises 1–30, find the domain of each function. f(x) = x² - 2x - 15
True or false defines y as a function of x.______ 2 y = ± √x² - 1 +
In Exercises 1–6, determine whether each relation is a function. Give the domain and range for each relation. ... ............ -4... -2... *+ y 2. 4. 6000 I X
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
In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form. y = -2x y INDY (-1, 2) IN L ECCE L is perpendicular to y = -2x.
Fill in each blank so that the resulting statement is true.The graph of an equation is symmetric with respect to the_____ if substituting -y for y in the equation results in an equivalent equation
Fill in each blank so that the resulting statement is true.The equation x2 + y2 + Dx + Ey + F = 0 is called the_______ form of the equation of a circle.
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
In Exercises 1–6, determine whether each relation is a function. Give the domain and range for each relation. X C K + ILI ***********...
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) = 4x + 9 and g(x) = X 4
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = f(x - 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.(2, -3) and (-1, 5)
In Exercises 1–30, find the domain of each function. g(x) 2 x + 5
Fill in each blank so that the resulting statement is true.If a line falls from left to right, the line has_______ slope.
True or false: y = x2 - 1 defines y as a function of x._______
In Exercises 1–10, determine whether each relation is a function.Give the domain and range for each relation. {(3, 4), (3, 5), (4,4), (4,5)}
Fill in each blank so that the resulting statement is true.Consider the line whose equation is y = -1/3 x + 5. The slope of any line that is parallel to this line is______ . The slope of any line
In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form. S y y = 2x QUID (2,4) L X L is perpendicular to y = 2x.
Fill in each blank so that the resulting statement is true.The standard form of the equation of a circle with center (h, k) and radius r is_________ .
Fill in each blank so that the resulting statement is true.The graph of f -1 is a reflection of the graph of f about the line whose equation is_________ .
Fill in each blank so that the resulting statement is true.(f - g)(x) =__________ .
In Exercises 1–10, determine whether each relation is a function.Give the domain and range for each relation. {(5, 6), (5,7), (6, 6), (6, 7))
Fill in each blank so that the resulting statement is true.Consider the line whose equation is 2x + y - 6 = 0. The slope of any line that is parallel to this line is_______ . The slope of any line
Fill in each blank so that the resulting statement is true.The graph of y = f(-x) is the graph of y = f(x) reflected about the______.
Fill in each blank so that the resulting statement is true.The set of all points in a plane that are equidistant from a fixed point is a/an_________ . The fixed point is called the________ . The
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)= 3x + 8 and g(x) = x 8 3
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = f(x) - 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

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