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mathematics
precalculus
Precalculus 9th edition Michael Sullivan - Solutions
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 respect to the x-axis, the y-axis, or the origin У 3 -3 3х -3
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 respect to the x-axis, the y-axis, or the origin У -3 3 X -3
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 respect to the x-axis, the y-axis, or the origin Ул 3 -3 3х -3
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 double the value of an IRA that compounds annually at the rate of 12%?(b) 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 government financed the stimulus through EE bonds, how much would it have to pay back in 2029? How much
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 Уд y = e* • (2, e²) 6 3 (1, e) (-1, ;) (0, 1) y=0 (-2,) 3 х
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 of g.f(x) = x; g(x) = x
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 asymptote of g-1.(c) On the same graph as g, graph g-1.
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 – 1(f) y = log3(x - 1)(g) y = log3(1 - x)(h) y = 1 - log3 x Уд 3 X. -3-
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 return of 8% compounded annually, what should they pay for the bond?Problem involves zero-coupon bonds.
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 Уд y = e* • (2, e²) 6 3 (1, e) (-1, ;) (0, 1) y=0 (-2,) 3 х
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. The seller offers them three interest options on the second mortgage:(a) Simple interest at 12% per
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 5.9% each year, what will be the average cost of college at a 4-year private college for the
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 or to be given $1325 after 3 years?
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 continuously. Who has more money after 20 years, Will or Henry?
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 5.25% compounded monthly. How much does Kim have in the passbook account on May 1?
Solve exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.22x + 2x - 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) = 3x
In problem, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = 2 + 4x-1
Jim places $1000 in a bank account that pays 5.6% compounded continuously. After 1 year, will he have enough money to buy a computer system that costs $1060? If another bank will pay Jim 5.9% compounded monthly, is this a better deal?
Solve exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.ex+3 = πx
In problem, the graph of a one-to-one function f is given. Draw the graph of the inverse function f-1. For convenience (and as a hint), the graph of y = x is also given. -2 -2F
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