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mathematics
precalculus

Questions and Answers of Precalculus

True or FalseFor y = 2 sin(πx), the amplitude is 2 and the period is π/2.
What is the y-intercept of y = tan x? If necessary, refer to the graphs to answer each question.
The range of the sine function is _________.
Find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = -3 sin 2x +
Find the exact value of each expression.sin π/6
The _______ function takes as input a real number at that corresponds to a point P = (x, y) on the unit circle and outputs the x-coordinate.
180° = ____ radians.Fill in the above blank.
Sketch a graph of each of the following functions. Label at least three points on each graph.(a) y = x2(b) y = x3(c) y = ex(d) y = ln x(e) y = sin x(f) y = tan x
Convert angle in radians to degrees.2π/3
True or FalseThe graphs of y = sin x and y = cos x are identical except for a horizontal shift.
True or FalseThe graphs of y = tan x, y = cot x, y = sec x, and y = csc x each have infinitely many vertical asymptotes.
The domain of the tangent function is _____.
Find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 3 cos(2x + π)
Convert angle in radians to degrees.3π/4
If (x, y) is a point on the unit circle in quadrant IV and if x = √3/2, what is y?
On a circle of radius r, a central angle of radians subtends an arc of length s = _______; the area of the sector formed by this angle θ is A = ________.
Use transformations to graph the function y = (x - 3)2 + 2.
Convert angle in radians to degrees.3π/2
The function y = 3 cos(6x) has amplitude ________ and period ________.
It is easiest to graph y = sec x by first sketching the graph of __________.
The sine, cosine, cosecant, and secant functions have period ____________ ; the tangent and cotangent functions have period _______.
Find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. TT y = 2 cos 3x + 2
Convert angle in radians to degrees.9π/2
What point is symmetric with respect to the y-axis to the point (1/2, √3/2)?
If the radius of a circle is r and the length of the arc subtended by a central angle is also r, then the measure of the angle is 1 _______.
Discuss the equation x2 + y2 - 2x + 4y - 4 = 0. Graph it.
Convert angle in degrees to radians. Express your answer as a multiple of π.15°
The function y = A sin(ωx), A > 0, has amplitude 3 and period 2; then A _______ = and ω ______ .
The graph of y = sec x is symmetric with respect to the __________ and has vertical asymptotes at _______.
True or FalseThe equation x2 + 2x = (x + 1)2 - 1 is an identity.
Find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 3 sin(3x – π)
Convert angle in radians to degrees.-π/8
If two triangles are similar, then corresponding angles are ________ and the lengths of corresponding sides are _________.
Discuss the equation 2x - 3y = 12. Graph it.
Find an equation for a circle of radius 4 and center at the point (0, -2).
Convert angle in degrees to radians. Express your answer as a multiple of π.18°
The maximum value of y = sin x, 0 ≤ x ≤ 2π, is ___________ and occurs at x = __________.
The graph of y = tan x is symmetric with respect to the ________ and has vertical asymptotes at _________.
True or FalseThe function f(x) = √x is even.
Find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.y = 4 sin(2x – π)
Convert each angle in degrees to radians. Express your answer as a multiple of π.13°
True or FalseFor a function y = f(x), for each x in the domain, there is exactly one element y in the range.
An angle θ is in ____________ ___________ if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.
Find an equation for the line with slope -3 containing the point (-2, 5).
Convert angle in degrees to radians. Express your answer as a multiple of π.210°
Use transformations to graph y = √2x.
True or FalseIf x = 3 is a vertical asymptote of a rational function R, then limx→3 |R(x)| = ∞.
A function for which f(x) = f(-x) for all x in the domain of f is called a(n) _________ function.
True or FalseOnly two data points are required by a graphing utility to find the sine function of best fit.
Convert each angle in degrees to radians. Express your answer as a multiple of π.-400°
The value of the function f(x) = 3x - 7 at 5 is ________.
Find the real solutions, if any, of the equation 2x2 + x - 1 = 0.
Convert angle in degrees to radians. Express your answer as a multiple of π.135°
Use transformations to graph y = 3x2.
The domain of the function f(x) = x + 1/2x + 1 is ____________.
For the graph of y = A sin(ωx – ϕ), the number ϕ/ω is called the _____ ______.
Convert each angle in degrees to radians. Express your answer as a multiple of π.260°
In a right triangle, with legs a and b and hypotenuse c, the Pythagorean Theorem states that ________.
If a particle has a speed of r feet per second and travels a distance d (in feet) in time t (in seconds), then d = _________.
What is the formula for the circumference C of a circle of radius r? What is the formula for the area A of a circle of radius r?
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range(b) The intercepts, if any(c) Any symmetry with
The formulacan be used to find the number of years t required to multiply an investment m times when r is the per annum interest rate compounded n times a year.(a) How many years will it take to
If Pat pays $12,485.52 for a $25,000 face-value, zero-coupon bond that matures in 8 years, what is his annual rate of return?
In February 2009, President Obama signed into law a $787 billion federal stimulus package. At that time, 20-year Series EE bonds had a fixed rate of 1.3% compounded semiannually. If the federal
In problem, begin with the graph of y = ex[Figure 27] and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = e-xFigure 27
In problem, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.1.2x = (0.5)-x
In problem, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = 3x-1
In problem, for the given functions f and g, find:f(x) = x2 + 4; g(x) = √x - 2
In problem, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x)) = x. Give any values of x that need to be excluded from the domain of f and the domain
For the function g(x) = 3x + 2:(a) Graph g using transformations. State the domain, range, and horizontal asymptote of g.(b) Determine the inverse of g. State the domain, range, and vertical
Solve equation. (1/4)x = 1/64
In problem, the graph of a logarithmic function is given. Match each graph to one of the following functions:(a) y = log3 x(b) y = log3(-x)(c) y = -log3 x(d) y = -log3(-x)(e) y = log3 x â€“ 1(f)
In problem, the function f is one-to-one. Find its inverse and check your answer. Зх + 1 f(x) = х
Solve equation.3-x = 81
A child’s grandparents are considering buying a $40,000 face-value, zero-coupon bond at birth so that she will have enough money for her college education 17 years later. If they want a rate of
Find a so that the graph of f(x) = loga x contains the point (1/2, -4).
In problem, find functions f and g so that f ° g = H.H(x) = (1 + x2)3
In problem, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.9x - 3x+1 + 1 = 0
In problem, begin with the graph of y = ex[Figure 27] and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = -exFigure 27
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = x3 + 1
Colleen and Bill have just purchased a house for $650,000, with the seller holding a second mortgage of $100,000.They promise to pay the seller $100,000 plus all accrued interest 5 years from now.
In problem, find functions f and g so that f ° g = H.H(x) = (2x + 3)4
Solve exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.16x + 4x+1 - 3 = 0
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = x3 – 1
The average annual cost of college at 4-year private colleges was $25,143 in the 2008–2009 academic year. This was a 5.9% increase from the previous year.(a) If the cost of college increases by
In problem, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.22x + 2x + 2 - 12 = 0
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = 1 - 3x
In problem, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = 1 - 2-x/3
Suppose that April has access to an investment that will pay 10% interest compounded continuously.Which is better: to be given $1000 now so that she can take advantage of this investment opportunity
Solve exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.32x + 3x + 1 - 4 = 0
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = 4x + 2
In problem, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = 2 + 3x/2
Will invests $2000 in his IRA in a bond trust that pays 9% interest compounded semiannually. His friend Henry invests $2000 in his IRA in a certificate of deposit that pays 8½%compounded
Solve exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.32x + 3x - 2 = 0
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = -4x
In problem, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = 1 - 2x+3
On January 1, Kim places $1000 in a certificate of deposit that pays 6.8% compounded continuously and matures in 3 months. Then Kim places the $1000 and the interest in a passbook account that pays
Solve exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.22x + 2x - 12 = 0

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