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college algebra
Questions and Answers of
College Algebra
Decide whether or not each equation has a circle as its graph. If it does, give the center and the radius.x2 + y2 - 4x + 2y = 4
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Through (5, -8), m = 0
For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ.P(8, 2), Q(3, 5)
Find the center and radius of each circle.2x2 + 2y2 + 14x + 6y + 2 = 0
For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3). f(x) = (2x x-1 if x = -1 ifx>-1
Describe how the graph of ƒ(x) = -2√x + 2 - 3 can be obtained from the graph of y = √x.
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center (-2, 5), radius 4
Decide whether each relation defines a function.x.................................. y3................................ -47................................ -410.............................. -4
Decide whether or not each equation has a circle as its graph. If it does, give the center and the radius.x2 + y2 + 6x + 10y + 36 = 0
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Through (-3, 12), m = 0
Graph each linear function. Give the domain and range. Identify any constant functions.ƒ (x) = 3
For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ.P(-8, 4), Q(3, -5)
Find the center and radius of each circle.3x2 + 3y2 + 33x - 15y = 0
For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3). f(x) = = fx-2 ifx
Determine whether the graph of 3x2 - 2y2 = 3 is symmetric with respect to the (a) x-axis (b) y-axis (c) origin.
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center (4, 3), radius 5
Decide whether each relation defines a function.x ...................................y-4................................ √20................................. √24.................................
Decide whether or not each equation has a circle as its graph. If it does, give the center and the radius.x2 + y2 - 12x + 20 = 0
For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3). f(x) = 2 + x ifx 2
Let ƒ(x) = 2x2 - 3x + 2 and g(x) = -2x + 1. Find each of the following. Simplify the expressions when possible.(a) (ƒ - g)(x) (b) (f/g) (x)(c) domain of f/g(d) (e) (ƒ + g)(1) (f)
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center (5, -4), radius 7
Decide whether each relation defines a function, and give the domain and range.{(1, 1), (1, -1), (0, 0), (2, 4), (2, -4)}
Decide whether or not each equation has a circle as its graph. If it does, give the center and the radius.x2 + y2 + 2x + 16y = -61
For the pair of functions defined, find (ƒ + g) (x), (ƒ - g) (x), (ƒg) (x), and (f/g) (x). Give the domain of each.ƒ(x) = 6 - 3x, g(x) = -4x + 1
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Through (2, 3) and (-1, 2)
Write the equation of the linear function ƒ with graph having slope 9 and passing through the origin. Give the domain and range.
For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ.P(6, -2), Q(4, 6)
For the pair of functions defined, find (ƒ + g) (x), (ƒ - g) (x), (ƒg) (x), and (f/g) (x). Give the domain of each.ƒ(x) = 3x + 4, g(x) = 2x - 5
Let ƒ(x) = x2 + 3 and g(x) = -2x + 6. Find each of the following.(f/g) (5)
Let ƒ(x) = x2 + 3 and g(x) = -2x + 6. Find each of the following.(f/g) (-1)
Write an equation for each of the following, and sketch the graph.The line through the origin and perpendicular to the line 3x - 4y = 2
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center (0, 4), radius 4
Determine the intervals of the domain over which each function is continuous. 3. (3, 1) х -3 3
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center (3, 0), radius 3
Graph each linear function. Give the domain and range. Identify any constant functions.ƒ (x) = -4
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Through (5, 1), undefined slope
Let ƒ(x) = x2 + 3 and g(x) = -2x + 6. Find each of the following.(ƒg) (-3)
Graph each linear function. Give the domain and range. Identify any constant functions.ƒ (x) = -2x
Describe how the graph of ƒ(x) = 2(x + 1)3 - 6 compares to the graph of y = x3.
Find the center and radius of each circle.x2 + y2 - 4x + 6y + 12 = 0
Give three ordered pairs from each table.Number of U.S. Viewers of the Super BowlYear ......................Viewers (millions)2002................................
Match each equation with the sketch of its graph in A–I. (a) y = |x – 2| (b) y = |x| – 2 (c) y = |x| + 2 (f) y = |-x| (i) y = |x + 2|– 2 (e) y = -|x| (h) y = |x – 2|+ 2 (d) y = 2|x| (g) y =
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Through (-8, 4), undefined slope
Graph each linear function. Give the domain and range. Identify any constant functions.ƒ (x) = 3x
Let ƒ(x) = x2 + 3 and g(x) = -2x + 6. Find each of the following.(ƒg) (4)
Give three ordered pairs from each table.Percent of High School Students Who SmokeYear.................................. Percent1999.....................................
Let ƒ(x) = x2 + 3 and g(x) = -2x + 6. Find each of the following.(ƒ - g) (4)
Graph each linear function. Give the domain and range. Identify any constant functions. 2 f(x) = x 3 -x+ 2
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Through (-4, 3), m = 3/4
Match each equation with the sketch of its graph in A–I. (a) y = Vx + 3 (b) y= Vx – 3 (c) y= Vx+ 3 (d) y = 3Vx (e) y = – Vx (f) y= Vx – 3 (h) y = Vx + 3 + 2 (i) y = Vx – 3 – 2 (g) y= Vx
Use each graph to determine an equation of the circle. Express in center-radius form. (4, 9) (5, 6) х
Determine the intervals of the domain over which each function is continuous. х *(0, –1)
Write an equation for each of the following, and sketch the graph.The vertical line through (-4, 3)
Decide whether each relation defines a function.{(2, 4), (0, 2), (2, 6)}
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it.Center (2, 0), radius 6
Graph each function.ƒ(x) = |x - 2| - 1
Determine the intervals of the domain over which each function is continuous. (0, 3) х
Use each graph to determine an equation of the circle. Express in center-radius form. (-2, 6) (0, 3) х
Match each equation with the sketch of its graph in A–I. (b) у %3Dх? — 2 (c) y = (x + 2)² (a) y = x² + 2 (d) у %3 (х — 2)? (g) y = (x – 2)² + 1 (e) y = 2x² (f) y = –x² (h) y = (x +
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Through (-5, 4), m = - 3/2
Graph each linear function. Give the domain and range. Identify any constant functions. f(x) =-x -
Let ƒ(x) = x2 + 3 and g(x) = -2x + 6. Find each of the following.(ƒ - g) (-1)
Write an equation for each of the following, and sketch the graph.The line through (3, -5) with slope - 5/6
Decide whether each relation defines a function.{(8, 0), (5, 7), (9, 3), (3, 8)}
Determine the intervals of the domain over which each function is continuous. y НH
Consider the graph of the function shown here. Give the open interval(s) over which the function is.(a) Increasing(b) Decreasing(c) Constant (d) Continuous.(e) What is the domain of this
Use each graph to determine an equation of the circle. Express in center-radius form. (-2, 3) х
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Through (2, 4), m = -1
Give three ordered pairs from each table. y 3 3 -21 -5 18 4 6. -6
Graph each linear function. Give the domain and range. Identify any constant functions.ƒ(x) = -x + 4
Let ƒ(x) = x2 + 3 and g(x) = -2x + 6. Find each of the following.(ƒ + g) (-5)
Write an equation for each of the following, and sketch the graph.The circle with center (0, 2) and tangent to the x-axis
For each given slope, identify the line in A–D that could have this slope.-3 A. B. C. D. х х х х
For each given slope, identify the line in A–D that could have this slope.0 A. B. C. D. х х х х
For each given slope, identify the line in A–D that could have this slope.3 A. B. C. D. х х х х
For each given slope, identify the line in A–D that could have this slope.Undefined A. B. C. D. х х х х
Decide whether each relation defines a function.((5, 1), (3, 2), (4, 9), (7, 8)}
For Exercises 6–8, refer to the graph of ƒ(x) = |x + 3|.Give the largest open interval over which the function ƒ is(a) Decreasing, (b) Increasing, (c) Constant. y D (x) = |x+ 3[] |(-1,
Whether each statement is true or false. If false, explain why.The graph of y = x2 - 2 has two x-intercepts.
Graph each function.ƒ(x) = -x3 + 1
Graph each function. S Vĩ f(x) 2x + 3 if x
Fill in the blank(s) to correctly complete each sentence.The circle with center (3, 6) and radius 4 has equation _____________.
In the following exercises, (a) Find the center-radius form of the equation of each circle described, and (b) Graph it.Center (0, 0), radius 6
Determine the intervals of the domain over which each function is continuous. y х
Find the slope-intercept form of the equation of the line passing through (2, 3) and.(a) Parallel to the graph of y = -3x + 2(b) Perpendicular to the graph of y = -3x + 2.
Use each graph to determine an equation of the circle. Express in center-radius form. (3, 5) х
Match each equation in Column I with a description of its graph from Column II as it relates to the graph of y = x2. П A. a translation 7 units to the left B. a translation 7 units to the right C. a
Write an equation for each line described. Give answers in standard form for and in slope-intercept form (if possible).Through (1, 3), m = -2
Give three ordered pairs from each table. х -5 -1 -9 5 -17 -21
Graph each linear function. Give the domain and range. Identify any constant functions.ƒ(x) = x - 4
Let ƒ(x) = x2 + 3 and g(x) = -2x + 6. Find each of the following.(ƒ + g) (3)
Write an equation for each of the following, and sketch the graph.The circle with center (2, -1) and radius 3
Fill in the blank(s) to correctly complete each sentence.The largest open interval over which the function graphed here decreases is ____________. (3, 1) 3
Answer each question.How many points lie on the graph of x2 + y2 = -100?
To answer each question, refer to the following basic graphs.Which graphs of functions decrease over part of the domain and increase over the rest of the domain? On what open intervals do they
Find the center-radius form of the equation for each circle.Center (3, -6), tangent to the x-axis
Suppose point A has coordinates (5, -3). What is the equation of the.(a) Vertical line through A? (b) Horizontal line through A?
Fill in the blank(s) to correctly complete each sentence.The graph of x = y2 is the same as the graph of x = (-y)2 because reflecting it across the -axis yields the same ordered pairs.
The graph shows a straight line segment that approximates new motor vehicle sales in the United States from 2009 to 2013. Determine the average rate of change from 2009 to 2013, and interpret the
Whether each statement is true or false. If false, explain why.The distance between the points (0, 0) and (4, 4) is 4.
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