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Questions and Answers of College Algebra

Find a so that the point (-1, 2) is on the graph of f(x) = ax2 + 4.
True or False Every graph represents a function.
A quotient is considered rationalized if its denominator has no __________.
For a function y = f(x), the variable x is the _______ variable, and the variable y is the _____________ variable.
If a function is defined by an equation in x and y, then the set of points (x, y) in the xy-plane that satisfy the equation is called the __________.(a) Romain of the function (b) Range of the
The independent variable is sometimes referred to as the _____ of the function. (a) Range.(b) Value.(c) Argument.(d) Definition.
The graph of a function y = f(x) can have more than one of which type of intercept?(a) X-intercept (b) Y-intercept (c) Both (d) Neither
True or False If x is in the domain of a function f, we say that f is not defined at x, or f(x) does not exist.
When written as y = f(x), a function is said to be defined ___________.
The density of a gas under constant pressure depends on temperature. Holding pressure constant at 14.5 pounds per square inch, a chemist measures the density of an oxygen sample at temperatures of 0,
The table shows life expectancy at birth in the United States for selected years.(a) Does the table define a function?(b) What are the domain and range?(c) Call this function f. Give two ordered
Write an equation of the line passing through the given points. Give the final answer in standard form. 12 1 ( 17/₁-6) -6 and
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain.x - y < 3
Find the slope of each line, and sketch its graph. 4x - y = 4
Find the x- and y-intercepts. Then graph each equation.y - 5 = 0
Write an equation of the line passing through the given points. Give the final answer in standard form. and حاد ن
Find the slope of each line, and sketch its graph. y = 4x
Write an equation of the line passing through the given points. Give the final answer in standard form. 3 مه | نیا ام and مله 5' 3,
Graph each linear or constant function. Give the domain and range.H(x) = -3x
Each table of values gives several points that lie on a line.(a) What is the x-intercept of the line? The y-intercept?(b) Which equation in choices A–D corresponds to the given table of values?(c)
Find the slope of each line, and sketch its graph. y = -3x
Write an equation of the line passing through the given point and satisfying the given condition. (9,5); slope 0
Graph each linear or constant function. Give the domain and range.G(x) = 2x
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain. y = √x - 3
Find the slope of each line, and sketch its graph.x - 3 = 0
Each table of values gives several points that lie on a line.(a) What is the x-intercept of the line? The y-intercept?(b) Which equation in choices A–D corresponds to the given table of values?(c)
Write an equation of the line passing through the given point and satisfying the given condition. (-4,-2); slope 0
Graph each linear or constant function. Give the domain and range.g(x) = -4
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain. y = √x - 7
Each table of values gives several points that lie on a line.(a) What is the x-intercept of the line? The y-intercept?(b) Which equation in choices A–D corresponds to the given table of values?(c)
Find the slope of each line, and sketch its graph.x + 2 = 0
Write an equation of the line passing through the given point and satisfying the given condition. (9, 10); undefined slope
Graph each linear or constant function. Give the domain and range.ƒ(x) = 5
Find the slope of each line, and sketch its graph.y = -5
Find the midpoint of each segment with the given endpoints. (−8, 4) and (−2, −6)
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain. y = √2x + 9
Write an equation of the line passing through the given point and satisfying the given condition. (-2, 8); undefined slope
Find the midpoint of each segment with the given endpoints. (5,2) and (-1,8)
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain. y = x + 4 5
Find the midpoint of each segment with the given endpoints. (3, -6) and (6, 3)
Write an equation of the line passing through the given point and satisfying the given condition. 5 (-3,-2); slope 0
Find the slope of each line, and sketch its graph.y = -4
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain. y= x - 3 2 N
Find the midpoint of each segment with the given endpoints. (-10, 4) and (7,1)
Graph each linear or constant function. Give the domain and range.ƒ(x) = -2.5
Find the slope of each line, and sketch its graph.3x = 4
Find the slope of each line, and sketch its graph.2y = 3
Refer to the straight-line graph and work Exercises in order.Find ƒ(8). y ITO (-1,5) 2y=-3x + 7 NH ...0. (3,-1) X
Find the midpoint of each segment with the given endpoints. (-9, 3) and (9, 8)
Determine whether each relation defines y as a function of x. (Solve for y first if necessary.) Give the domain. у= 2 X
Graph each line passing through the given point and having the given slope. (-4, 2); m = 2/1/2
Write an equation of the line passing through the given point and satisfying the given condition. (-7, 8); horizontal
Evaluate each expression if possible. V0.49
Solve each system by graphing. x + 3y = 8 2x - y = 2
Assuming growth rates continue, the populations of Houston, Phoenix, Dallas, and Philadelphia will follow the trends indicated in the graph. Use the graph to work each problem.(a) Which of these
Evaluate each expression if possible. (-3)4
Solve each system by graphing. 2x + y = -8 x - 4y = -4
Suppose that a system has infinitely many ordered-triple solutions of the form (x, y, z) such thatGive three specific ordered triples that are solutions of the system. x + y + 2z = 1.
Assuming growth rates continue, the populations of Houston, Phoenix, Dallas, and Philadelphia will follow the trends indicated in the graph. Use the graph to work each problem.(a) In which year did
Without doing any algebraic work, but answering on the basis of knowledge of the graphs of the two lines, explain why the following system has Φ as its solution set. y = 3x + 2 y=3x-4
Suppose that two linear equations are graphed on the same set of coordinate axes. Sketch what the graph might look like if the system has the given description.(a) The system has a single
Explain what the following statement means: “The solution set of the following system is {(-1, 2, 3)}.” 2x + y + z = 3 3x - y + z = −2 -2 4xy + 2z = 0
If a container of liquid contains 60 oz of solution, what is the number of ounces of pure acid if the given solution contains the following acid concentrations?(a) 10% (b) 25% (c)
The following two equations have a common solution of (1, 2, 3).Which equation would complete a system of three linear equations in three variables having solution set {(1, 2, 3)}? x+y+z=6 2x = y + z
Solve each system by graphing. x - y = 2 x + 2y = -1
Evaluate each expression if possible. -(-3)4
Solve each system. -7x + 3y = 12 5x + 2y = 8
Solve the system by graphing. x+y=7 x-y=5
Solve each system. If a system is inconsistent or has dependent equations, say so. 2x - 3y = 24 y = 3₁ 2 -X
Which ordered pair is not a solution of the equation 3x + 2y = 6? A. (2,0) B. (0,3) C. (4, -3) D. (3,-2)
If $5000 is invested in an account paying simple annual interest, how much interest will be earned during the first year at the following rates?(a) 2% (b) 3% (c) 4% (d) 3.5%
What constant should replace the question mark in this system so that the solution set is {(1, 1, 1)}? 2x - 3y + -5x + 2y z = 0 - 2 = x + y + 2z = ? −4 -4
Evaluate each expression if possible.-34
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 3x+y=-4 2 у 3- X || с
Solve each system. x x + 2y = 48 1 x + 4 1 2 = 12
If one pound of turkey costs $1.99, how much will x pounds cost?
Complete the work of Example 1 and show that the ordered triple (-3, 1, 6) is also a solution of equations (2) and (3).Data from in Example 1 x + 7y - 32 = −14 3z 2x - 3y + 2z = 3 Equation
Solve each system. If a system is inconsistent or has dependent equations, say so. 3x - y = -8 2x + бу = 3
Evaluate each expression if possible. -V0.49
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 9x - y = -4 y = x + 4
If one movie ticket costs $13.50, how much will y tickets cost?
Complete each statement. If the two lines forming a system have the same slope and different y-intercepts, the system has (no / one / infinitely many) solution(s).
Solve each system. x + 4y = - 3x + 2y = 17 -9
Solve each system. If a system is inconsistent or has dependent equations, say so. 12x-5y=8 5 y + 2 3x = = У 4
If the rate of a boat in still water is 10 mph and the rate of the current of a river is x mph, what is the rate of the boat in each case?(a) The boat is going upstream (that is, against the current,
Complete each statement. If the two lines forming a system have different slopes, the system has (no / one / infinitely many) solution(s).
Evaluate each expression if possible. V-0.49
Solve each system. 2x - 5y + 32 = −1 x + 4y2z = 9 x - 2y4z = -5
If the rate of a plane in still air is x mph and the rate of a steady wind is 20 mph, what is the rate of the plane in each case?(a) The plane is flying into the wind (that is, into a headwind, which
Which ordered pair could be a solution of the graphed system of equations? Why? A. (4,4) B. (-4,4) C. (-4,-4) D. (4,-4) 0 X
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. -5x + 2y = -2 x + 6y = 26
Solve each system. 12/3 = 2 || - ताने + - बॉल नॉल
Solve each system. If a system is inconsistent or has dependent equations, say so. 3x + y = 12 2x - y = 3
A bear is running at a rate of 44 ft per sec.(a) If the bear runs for 5 sec, what is its distance?(b) If the bear travels d ft, what is its time?
Solve each system. x + 3y - 62 = 1 - 2x = y + z = 7 x + 2y + 2z = 14
Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. 5x + y = 2x - 2y = 12 0
Which ordered pair could be a solution of the graphed system of equations? Why? A. (4,0) B. (-4,0) C. (0,4) D. (0, -4) 0 X
Solve each system. x = 7y + 10 2x + 3y = 3
Solve each system. If a system is inconsistent or has dependent equations, say so. -5x + 2y = -4 6x + 3y = -6
Solve each system. 3x + 2y + z = 8 2x − 3y + 2z = −16 - z = 20 x + N 4y

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