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study help
mathematics
precalculus
Questions and Answers of
Precalculus
In problem, use the graph of the function f to solve the inequality.(a) f(x) > 0 (b) f(x) ¤ 0 y A 0 12
In the process of polynomial division, (Divisor)(Quotient) + ________ = ____________.
Find the equation of the line parallel to the line y = 2x + 1 and containing the point (3, 5). Express your answer in slope-intercept form and graph the line.
True or FalseThe x-intercepts of the graph of a function y = f(x) are the real solutions of the equation f(x) = 0.
True or FalseThe domain of every rational function is the set of all real numbers.
In problem, find the domain of each function. Find any horizontal, vertical, or oblique asymptotes. 2x2 14x + 24 8(x) = .2 x² + 6x – 40
True or Falsef(g(x)) = f(x) - g(x).
True or FalseThe graph of a rational function sometimes intersects an oblique asymptote.
If 3 + 4i is a zero of a polynomial function of degree 5 with real coefficients, then so is _____.
In problem, determine whether the function is a polynomial function, rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial
True or FalseThe graph of f(x) = x/x - 3 is above the x-axis for x < 0 or x > 3, so the solution set of the inequality x/x – 3 is {x|x ≤ 0 or x ≤ 3}.
Find the intercepts of f(x) = x2 + x - 3.
Find a linear function with slope -3 that contains the point (-1, 4). Graph the function.
Use a graphing utility to approximate (rounded to two decimal places) the local maximum value and local minimum value off(x) = x3 - 2x2 - 4x + 5, for -3 < x < 3.
Graph y = 2(x + 1)2 – 3 using transformations.
Solve 3x3 + 2x - 1 = 8x2 - 4 in the complex number system.
Given two functions f and g, the _______ ________, denoted f 0 g, is defined by f 0 g(x) = ______.
The graph of a rational function never intersects a ______ asymptote.
In problem, determine whether the function is a polynomial function, rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial
Every polynomial function of odd degree with real coefficients will have at least _________ real zero(s).
True or FalseA test number for the interval -2 < x < 5 could be 4.
Find the quotient and remainder if 3x4 - 5x3 + 7x - 4 is divided by x - 3.
Solve the inequality x2 - 3x < 4 and graph the solution set.
To graph y = x2 - 4, you would shift the graph of y = x2 a distance of units.
Find the complex zeros of f(x) = x3 – 4x2 + 25x - 100.
Find the domain of the function x - 1 x - 25 f(x) : .2
In problem, determine whether the function is a polynomial function, rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial
In the complex number system, find the complex solutions of the equation x2 + 2x + 2 = 0.
Solve the inequality x2 – 5x ≤ 24. Graph the solution set.
Factor the expression 6x2 + x - 2.
Solve the inequality x2 ≥ x and graph the solution set.
Is the expression 4x3 - 3.6x2 – √2 a polynomial? If so, what is its degree?
What are the quotient and remainder when 3x4 – x2 is divided by x3 - x2 + 1.
For the polynomial function g(x) = 2x3 + 5x2 - 28x - 15,(a) Determine the maximum number of real zeros that the function may have.(b) Find bounds to the zeros of the function.(c) List the potential
Find f(3x) if f(x) = 4 - 2x2.
In problem, determine whether the function is a polynomial function, rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial
Find the sum and the product of the complex numbers 3 – 2i and -3 + 5i.
Solve the inequality 3 – 4x > 5. Graph the solution set.
Find f(-1) if f(x) = 2x2 - x.
Find the distance between the points P = (1, 3) and Q = (-4, 2).
The intercepts of the equation 9x2 + 4y = 36 are _________.
True or FalseThe quotient of two polynomial expressions is a rational expression.
Graph f(x) = (x - 3)4 - 2 using transformations.
Find f(3) if f(x) = -4x2 + 5x.
Translate the following sentence into a mathematical equation: The total revenue R from selling x hot dogs is $3 times the number of hot dogs sold.
Is the following graph the graph of a function? УА х
Which of the following functions might have the graph shown?(a) f(x) = 2x - 7(b) g(x) = -3x + 4(c) H(x) = 5(d) F(x) = 3x + 4(e) G(x) = 1/2 x + 2 ул
Which of the following functions might have the graph shown?(a) f(x) = 3x + 1(b) g(x) = -2x + 3(c) H(x) = 3(d) F(x) = -4x - 1(e) G(x) = -2/3 x + 3 У4
Find the distance between the points P = (-1, 3) and Q = (4, -2). Find the midpoint of the line segment P to Q.
For the linear function f(x) = -4x + 3,(a) Find the slope and y-intercept.(b) What is the average rate of change of f?(c) Determine whether f is increasing, decreasing, or constant.(d) Graph f.
Which of the following points are on the graph of y = x3 - 3x + 1? (a) (-2, -1) (b) (2, 3) (c) (3, 1)
In problem, find the intercepts of each quadratic function.f(x) = 3x2 - 2x - 8
Solve the inequality 5x + 3 ≥ 0 and graph the solution set.
In problem, find the intercepts of each quadratic function.G(x) = -2x2 + 4x + 1
Find the equation of the line containing the points (-1, 4) and (2, -2). Express your answer in slope-intercept form and graph the line.
Given that f(x) = x2 + 3x and g(x) = 5x + 3, solve f(x) = g(x). Graph each function and label the points of intersection.
Find the equation of the line perpendicular to the line y = 2x + 1 and containing the point (3, 5). Express your answer in slope-intercept form and graph the line.
Graph f(x) = (x - 3)2 - 2 using transformations.
Graph the equation x2 + y2 - 4x + 8y -5 = 0.
For the quadratic function f(x) = 3x2 - 12x + 4,(a) Determine whether the graph opens up or down.(b) Determine the vertex.(c) Determine the axis of symmetry.(d) Determine the intercepts(e) Use the
Does the following relation represent a function?{(-3, 8), (1, 3), (2, 5), (3, 8)}.
Determine whether f(x) = -2x2 + 12x + 3 has a maximum or minimum value. Then find the maximum or minimum value.
For the function f defined by f(x) = x2- 4x + 1, find:(a) f(2)(b) f(x) + f(2)(c) f (-x)(d) -f(x)(e) f(x + 2)(f) f(x + h) – f(x) h + 0
Find the domain of h(z) = 3z – 1/6z - 7.
The weekly rental cost of a 20-foot recreational vehicle is $129.50 plus $0.15 per mile.(a) Find a linear function that expresses the cost C as a function of miles driven m.(b) What is the rental
Consider the function f(x) = x/x + 4(a) Is the point (1, 1/4) on the graph of f?(b) If x = -2, what is f(x)? What point is on the graph of f?(c) If f(x) = 2, what is x? What point is on the graph of
Is the function f(x) = x2/2x + 1 even, odd, or neither?
Approximate the local maximum values and local minimum values of f(x) = x3 - 5x + 1 on (-4, 4). Determine where the function is increasing and where it is decreasing.
If f(x) = 3x + 5 and g(x) = 2x + 1,(a) Solve f(x) = g(x).(b) Solve f(x) > g(x).
For the graph of the function f,(a) Find the domain and the range of f.(b) Find the intercepts.(c) Is the graph of f symmetric with respect to the x-axis, the y-axis, or the origin?(d) Find f(2).(e)
A pediatrician wanted to find a linear model that relates a child’s height,H, to head circumference, C. She randomly selects nine children from her practice, measures their height and head
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
In problem,(a) Graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.(b) Determine the
In problem, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.f(x) = 3x2 - 6x + 4
What does a correlation coefficient of 0 imply?
In problem, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.f(x) = 2x2 + 8x + 5
In problem, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value. f(x) = -x2 + 8x - 4
In problem, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.f(x) = -x2 - 10x – 3
In problem, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.f(x) = -3x2 + 12x + 4
In problem, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.f(x) = -2x2 + 4
In problem, use the given functions f and g.(a) Solve f(x) = 0.(b) Solve g(x) = 0.(c) Solve f(x) = g(x).(d) Solve f(x) > 0.(e) Solve g(x) ≤ 0.(f) Solve f(x) > g(x).(g) Solve f(x) ≥ 1.f(x) =
A cricket makes a chirping noise by sliding its wings together rapidly. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the
In parts (a) - (f), use the following figure.(a) Solve f(x) = 50.(b) Solve f(x) = 80.(c) Solve f(x) = 0.(d) Solve f(x) > 50.(e) Solve f(x) ¤ 80. (f) Solve 0 < f (x) < 80.
In problem, find the quadratic function for which:x2 + 6x - 16 < 0
In problem, use the given functions f and g.(a) Solve f(x) = 0.(b) Solve g(x) = 0.(c) Solve f(x) = g(x).(d) Solve f(x) > 0.(e) Solve g(x) ≤ 0.(f) Solve f(x) > g(x).(g) Solve f(x) ≥ 1.f(x) =
Refer to Example 1 on page 146. Notice that if the price charged for the calculators is $0 or $140 the revenue is $0. It is easy to explain why revenue would be $0 if the price charged is $0, but how
In problem, find the quadratic function for which:3x2 − 2x −1≥ 0
In problem, use the given functions f and g.(a) Solve f(x) = 0.(b) Solve g(x) = 0.(c) Solve f(x) = g(x).(d) Solve f(x) > 0.(e) Solve g(x) ≤ 0.(f) Solve f(x) > g(x).(g) Solve f(x) ≥ 1.f(x) =
In problem, solve each quadratic inequality.3x2 ≥ 14x + 5
A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s(t) = 80t – 16t2.(a) At what time t will
In parts (a) and (b), use the following figure.(a) Solve the equation: f(x) = g(x).(b) Solve the inequality: f(x) ¤ g(x). (y = f(x) - (2, 5) y = g(x)
In problem, solve each quadratic inequality.4x2 < 13x - 3
A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s(t) = 96t – 16t2.(a) At what time t will
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) isR(p) = -4p2 + 4000 p(a) At what prices p is revenue zero?(b) For
In problem, find the quadratic function for which:Vertex is (3, -4); contains the point (4, 2)
The John Deere company has found that the revenue from sales of heavy-duty tractors is a function of the unit price p, in dollars, that it charges. If the revenue R, in dollars, is(a) At what prices
Marissa must decide between one of two companies as her long distance phone provider. Company A charges a monthly fee of $7.00 plus $0.06 per minute, while Company B does not have a monthly fee, but
A projectile fired from the point (0, 0) at an angle to the positive x-axis has a trajectory given bywherex = horizontal distance in metersy = height in metersv = initial muzzle velocity in meters
Using Hooke's Law, we can show that the work done in compressing a spring a distance of x feet from its at-rest position is W = 1/2kx2, where k is a stiffness constant depending on the spring. It can
Bill was just offered a sales position for a computer company. His salary would be $15,000 per year plus 1% of his total annual sales.(a) Find a linear function that relates Bill’s annual salary,
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