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mathematics
college algebra
Questions and Answers of
College Algebra
Determine whether each function is even, odd, or neither.(a) ƒ(x) = x2 - 7(b) ƒ(x) = x3 - x - 1(c) ƒ(x) = x101 - x99
Refer to functions ƒ and g as described in Exercises, and find the following.Domain of ƒ/g
Write an equation for each of the following, and sketch the graph.The horizontal line through (2, 3)
Answer each question.How many points lie on the graph of x2 + y2 = 0?
Fill in the blank(s) to correctly complete each sentence.The largest open interval over which the function graphed here increases is ______________.
To answer each question, refer to the following basic graphs.Which one is discontinuous at many points? What is its range? C. A. B. 123 -8 F. E. D. Ho х G. Н. I. 8. 2- -2 8. -2 2.
Find the center-radius form of the equation for each circle.Center (-8, 1), passing through (0, 16)
In each case, determine whether y is a function of x. Give the domain and range. If it is a function, give the largest open intervals over which it is increasing, decreasing, or constant. (b) 4- х
Match each equation with its graph in A–D.y = 4 А. В. (0, 4) F(0, 4) (3, 0) С. D. (0, 2 312 (1, -1) (-1,-4) 十中十
Match each equation with its graph in A–D. 3 y - (-1) = -(x – 1)
Fill in the blank(s) to correctly complete each sentence.The graph of ƒ(x) = |-x| is the same as the graph of y = |x| because reflecting it across the -axis yields the same ordered pairs.
Find the slope of the line through the given points.(a) (1, 5) and (5, 11) (b) (-7, 4) and (-1, 4) (c) (6, 12) and (6, -4)
Whether each statement is true or false. If false, explain why.The midpoint of the segment joining (0, 0) and (4, 4) is 2.
The function g(x) graphed here is obtained by stretching, shrinking, reflecting, and/or translating the graph of ƒ(x) = √x. Give the equation that defines this function. -2
Refer to functions ƒ and g as described in Exercises, and find the following.Domain of ƒ + g
Write an equation for each of the following, and sketch the graph.The line through (-2, 1) and (4, -1)
Match each equation in Column I with its graph in Column II.(x + 3)2 + (y + 2)2 = 25 A. B. y х -2 C. D. .10 -2 -3.10
Fill in the blank(s) to correctly complete each sentence.The function in Exercise 6 has range ______________.
To answer each question, refer to the following basic graphs.Which one is the graph of ƒ(x) = √x? What is its domain? C. A. B. 123 -8 F. E. D. Ho х G. Н. I. 8. 2- -2 8. -2 2.
Find the center-radius form of the equation for each circle.Center (√5, -√7), radius √3
Graph the circle with equation x2 + y2 + 4x - 10y + 13 = 0.
Match each equation with its graph in A–D.4x + 3y = 12 A. B. (0, 4) -(0, 4) (3, 0) х C. D. (0, 2) HН ИН- х х (1, –1) 3! (-1, –4)
Fill in the blank(s) to correctly complete each sentence.To obtain the graph of ƒ(x) = (x - 3)3 + 6, shift the graph of y = x3 to the right units and up units.
Graph each function.ƒ(x) = 2|x - 1| + 3
Refer to functions ƒ and g as described in Exercises, and find the following.Domain of g
For the points P and Q, find (a) The distance d(P, Q), (b) The coordinates of the midpoint of the segment PQ, (c) An equation for the line through the two points. Write the equation in
Match each equation in Column I with its graph in Column II. (x + 3)2 + (y - 2)2 = 25
To answer each question, refer to the following basic graphs.Which one is the graph of ƒ(x) = 3√x? Is there any open interval over which the function is decreasing? C. A. B. 123 -8 F. E. D. Ho х
Fill in the blank(s) to correctly complete each sentence.The function in Exercise 6 has domain _____________.
Find the center-radius form of the equation for each circle.Center (-2, 3), radius 15
Use each graph to determine an equation of the circle. Express it in center-radius form. (b) (a) (1, 4) 2. х х +++
Match each equation with its graph in A–D. 1 y=-x + 2 +2 4
For Exercises 6–8, refer to the graph of ƒ(x) = |x + 3|.Give the domain and the range of ƒ.
Whether each statement is true or false. If false, explain why.The graph of y = x2 + 2 has no x-intercepts.
Fill in the blank(s) to correctly complete each sentence.To obtain the graph of ƒ(x) = (x + 2)3 - 3, shift the graph of y = x3 to the left units and down units.
Refer to functions ƒ and g as described in Exercises, and find the following.Domain of ƒ
For the points P and Q, find (a) The distance d(P, Q), (b) The coordinates of the midpoint of the segment PQ, (c) An equation for the line through the two points. Write the equation in
Match each equation in Column I with its graph in Column II.(x - 3)2 + (y + 2)2 = 25 A. В. y -. C. D. 2.
To answer each question, refer to the following basic graphs.Which one is the graph of ƒ(x) = [[x]]? What is the function value when x = 1.5? C. A. B. 123 -8 F. E. D. Ho х G. Н. I. 8. 2- -2 8. -2
Use the distance formula to determine whether the points (-2, -5), (1, 7), and (3, 15) are collinear.
Fill in the blank(s) to correctly complete each sentence.For the function g(x) = √x, g(9) = _________________.
The graph shows the line that passes through the points (-2, 1) and (3, 4).Write the linear function ƒ(x) = ax + b that has this line as its graph. (3, 4) (-2, 1) Hн х
Fill in the blank(s) to correctly complete each sentence.Any line perpendicular to the graph of 6x + 7y = 9 must have slope ________.
For Exercises 6–8, refer to the graph of ƒ(x) = |x + 3|.Find ƒ(-1).
Fill in the blank to correctly complete each sentence.The distance from the origin to the point (-3, 4) is ____________.
Fill in the blank(s) to correctly complete each sentence.The graph of ƒ(x) = √-x is a reflection of the graph of y = √x across the -axis.
Match the description in Column I with the correct response in Column II. Some choices may not be used.A function that is not linear A. f(x) = 5x В. f(x) — Зх + 6 С. f(х) — —8 D. f(x) —
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x) = x + 1 and g(x) = x2(g ° ƒ) (2)
For the points P and Q, find (a) The distance d(P, Q), (b) The coordinates of the midpoint of the segment PQ, (c) An equation for the line through the two points. Write the equation in
Match each equation in Column I with its graph in Column II.(x - 3)2 + (y - 2)2 = 25 A. B. y х -2 C. D. .10 -2 -3.10
To answer each question, refer to the following basic graphs.Which one is the identity function? What is its equation? C. A. B. 123 -8 F. E. D. Ho х G. Н. I. 8. 2- -2 8. -2 2.
Determine the coordinates of B for line segment AB, given that A has coordinates (-6, 10) and the coordinates of its midpoint M are (8, 2).
Fill in the blank(s) to correctly complete each sentence.For the function ƒ(x) = -4x + 2, ƒ(-2) = ____________.
The graph shows the line that passes through the points (-2, 1) and (3, 4).Find the standard form of the equation of the line. (3, 4) (-2, 1) Hн х
Fill in the blank(s) to correctly complete each sentence.Any line parallel to the graph of 6x + 7y = 9 must have slope____________.
Determine the radius and the coordinates of the center of the circle with equationx2 + y2 - 4x + 8y + 3 = 0.
Fill in the blank to correctly complete each sentence.The x-intercept of the graph of 2x + 5y = 10 is ______________.
A certain long-distance carrier provides service between Podunk and Nowheresville. If x represents the number of minutes for the call, where x > 0, then the function ƒ(x) = 0.40[[x]] + 0.75 gives
Fill in the blank(s) to correctly complete each sentence.The graph of ƒ(x) = -√x is a reflection of the graph of y = √x across the -axis.
Match the description in Column I with the correct response in Column II. Some choices may not be used.A linear function whose graph passes through the origin A. f(x) = 5x В. f(x) — Зх + 6 С.
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x) = x + 1 and g(x) = x2 (ƒ ° g) (2)
For the points P and Q, find (a) The distance d(P, Q), (b) The coordinates of the midpoint of the segment PQ, (c) An equation for the line through the two points. Write the equation in
Fill in the blank(s) to correctly complete each sentence.The graph of x2 + (y - 5)2 = 9 has center with coordinates ______________.
To answer each question, refer to the following basic graphs.Which one is not the graph of a function? What is its equation? C. A. B. 123 -8 F. E. D. Ho х G. Н. I. 8. 2- -2 8. -2 2.
Are the points (5, 7), (3, 9), and (6, 8) the vertices of a right triangle? If so, at what point is the right angle?
Fill in the blank(s) to correctly complete each sentence.The function in Exercise 3 includes the ordered pair (6, _____________).
The graph shows the line that passes through the points (-2, 1) and (3, 4).What are the coordinates of the midpoint of the line segment joining the two points? (3, 4) (-2, 1) Hн х
Fill in the blank(s) to correctly complete each sentence.The horizontal line through the point (-4, 8) has equation _______ = 8.
Graph x2 + y2 = 16.
Fill in the blank to correctly complete each sentence.The y-intercept of the graph of y = -2x + 6 is _____________.
For each basic function graphed, give the name of the function, the domain, the range, and open intervals over which it is decreasing, increasing, or constant. (c) (b) -8- х 8. -8
Fill in the blank(s) to correctly complete each sentence.The graph of ƒ(x) = (x - 7)2 is obtained by shifting the graph of y = x2 to the______ 7 units.
Match the description in Column I with the correct response in Column II. Some choices may not be used.A linear function whose graph has x-intercept (-2, 0) and y-intercept (0, 4) A. f(x) = 5x В.
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x) = x + 1 and g(x) = x2(f/g) (2)
For the points P and Q, find (a) The distance d(P, Q), (b) The coordinates of the midpoint of the segment PQ, (c) An equation for the line through the two points. Write the equation in
To answer each question, refer to the following basic graphs.Which one is the graph of ƒ(x) = x3? What is its range? C. A. B. 123 -8 F. E. D. Ho х G. Н. I. 8. 2- -2 8. -2 2.
Fill in the blank(s) to correctly complete each sentence.The graph of (x - 4)2 + (y + 7)2 = 9 has center with coordinates .
Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them.A(-6, 3), B(-6, 8)
Fill in the blank(s) to correctly complete each sentence.The equation y = 4x - 6 defines a function with independent variable and dependent variable _____________.
The graph shows the line that passes through the points (-2, 1) and (3, 4).What is the distance between the two points shown? (3, 4) (-2, 1) Hн х
Fill in the blank(s) to correctly complete each sentence.The vertical line through the point (-4, 8) has equation ________= -4.
Fill in the blank to correctly complete each sentence.Any point that lies on the x-axis has y-coordinate equal to ____________.
Suppose that P has coordinates (-8, 5). Find the equation of the line through P that is(a) Vertical (b) Horizontal.
Fill in the blank(s) to correctly complete each sentence.The graph of ƒ(x) = (x + 4)2 is obtained by shifting the graph of y = x2 to the________ 4 units.
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x) = x + 1 and g(x) = x2(ƒg) (2)
Match the description in Column I with the correct response in Column II. Some choices may not be used.A constant function A. f(x) = 5x В. f(x) — Зх + 6 С. f(х) — —8 D. f(x) — х? Е. х
For the points P and Q, find (a) The distance d(P, Q), (b) The coordinates of the midpoint of the segment PQ, (c) An equation for the line through the two points. Write the equation in
To answer each question, refer to the following basic graphs.Which one is the graph of ƒ(x) = 0 x 0 ? On what open interval is it increasing? C. A. B. 123 -8 F. E. D. Ho х G. Н. I. 8. 2- -2 8. -2
Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them.M(-8, 2), N(3, -7)
The graph shows the line that passes through the points (-2, 1) and (3, 4).What is the slope of the line? (3, 4) (-2, 1) Hн х
Fill in the blank(s) to correctly complete each sentence.The range of the relation in Exercise 1 is _____________.
Fill in the blank(s) to correctly complete each sentence.The graph of the line y = -2x + 7 has slope _____and y-intercept ________.
Enrollments in two-year colleges for selected years are shown in the table. Use the midpoint formula to estimate the enrollments for 2006 and 2010.Year.......................Enrollment (in
Fill in the blank to correctly complete each sentence.The point (4, _____) lies on the graph of the equation y = 3x - 6.
Find the slope-intercept form of the equation of the line passing through the point (-6, 4) and perpendicular to the graph of 3x - 2y = 6.
Fill in the blank(s) to correctly complete each sentence.To graph the function ƒ(x) = x2 + 5, shift the graph of y = x2 up _________units.
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x) = x + 1 and g(x) = x2(ƒ - g) (2)
Match the description in Column I with the correct response in Column II. Some choices may not be used.A vertical line A. f(x) = 5x В. f(x) — Зх + 6 С. f(х) — —8 D. f(x) — х? Е. х +
For the points P and Q, find (a) The distance d(P, Q), (b) The coordinates of the midpoint of the segment PQ, (c) An equation for the line through the two points. Write the equation in
To answer each question, refer to the following basic graphs.Which one is the graph of ƒ(x) = x2? What is its domain? C. A. B. 123 -8 F. E. D. Ho х G. Н. I. 8. 2- -2 8. -2 2.
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