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g

Domain: x > 5 , range: all real numbers

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g f

Domain: x > 2 and x < 4 , range: all real numbers

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Find the degree, y -intercept, and zeros for the following polynomial functions.

f ( x ) = 2 x 2 + 9 x 5

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f ( x ) = x 3 + 2 x 2 2 x

Degree of 3, y -intercept: 0, zeros: 0, 3 1 , −1 3

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Simplify the following trigonometric expressions.

tan 2 x sec 2 x + cos 2 x

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cos ( 2 x ) = sin 2 x

cos ( 2 x ) or 1 2 ( cos ( 2 x ) + 1 )

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Solve the following trigonometric equations on the interval θ = [ −2 π , 2 π ] exactly.

sec 2 x 2 sec x + 1 = 0

0 , ± 2 π

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Solve the following logarithmic equations.

Are the following functions one-to-one over their domain of existence? Does the function have an inverse? If so, find the inverse f −1 ( x ) of the function. Justify your answer.

f ( x ) = 1 x

One-to-one; yes, the function has an inverse; inverse: f −1 ( x ) = 1 y

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For the following problems, determine the largest domain on which the function is one-to-one and find the inverse on that domain.

f ( x ) = x 2 + 3 x + 4

x 3 2 , f −1 ( x ) = 3 2 + 1 2 4 y 7

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A car is racing along a circular track with diameter of 1 mi. A trainer standing in the center of the circle marks his progress every 5 sec. After 5 sec, the trainer has to turn 55° to keep up with the car. How fast is the car traveling?

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For the following problems, consider a restaurant owner who wants to sell T-shirts advertising his brand. He recalls that there is a fixed cost and variable cost, although he does not remember the values. He does know that the T-shirt printing company charges $440 for 20 shirts and $1000 for 100 shirts.

a. Find the equation C = f ( x ) that describes the total cost as a function of number of shirts and b. determine how many shirts he must sell to break even if he sells the shirts for $10 each.

a. C ( x ) = 300 + 7 x b. 100 shirts

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a. Find the inverse function x = f −1 ( C ) and describe the meaning of this function. b. Determine how many shirts the owner can buy if he has $8000 to spend.

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For the following problems, consider the population of Ocean City, New Jersey, which is cyclical by season.

The population can be modeled by P ( t ) = 82.5 67.5 cos [ ( π / 6 ) t ] , where t is time in months ( t = 0 represents January 1) and P is population (in thousands). During a year, in what intervals is the population less than 20,000? During what intervals is the population more than 140,000?

The population is less than 20,000 from December 8 through January 23 and more than 140,000 from May 29 through August 2

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In reality, the overall population is most likely increasing or decreasing throughout each year. Let’s reformulate the model as P ( t ) = 82.5 67.5 cos [ ( π / 6 ) t ] + t , where t is time in months ( t = 0 represents January 1) and P is population (in thousands). When is the first time the population reaches 200,000?

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For the following problems, consider radioactive dating. A human skeleton is found in an archeological dig. Carbon dating is implemented to determine how old the skeleton is by using the equation y = e r t , where y is the percentage of radiocarbon still present in the material, t is the number of years passed, and r = −0.0001210 is the decay rate of radiocarbon.

If the skeleton is expected to be 2000 years old, what percentage of radiocarbon should be present?

78.51%

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Find the inverse of the carbon-dating equation. What does it mean? If there is 25% radiocarbon, how old is the skeleton?

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Questions & Answers

any genius online ? I need help!!
Guzorochi Reply
how can i help you?
Pina
need to learn polynomial
Zakariya
i will teach...
nandu
I'm waiting
Zakariya
evaluate the following computation (x³-8/x-2)
Murtala Reply
teach me how to solve the first law of calculus.
Uncle Reply
what is differentiation
Ibrahim Reply
f(x) = x-2 g(x) = 3x + 5 fog(x)? f(x)/g(x)
Naufal Reply
fog(x)= f(g(x)) = x-2 = 3x+5-2 = 3x+3 f(x)/g(x)= x-2/3x+5
diron
pweding paturo nsa calculus?
jimmy
how to use fundamental theorem to solve exponential
JULIA Reply
find the bounded area of the parabola y^2=4x and y=16x
Omar Reply
what is absolute value means?
Geo Reply
Chicken nuggets
Hugh
🐔
MM
🐔🦃 nuggets
MM
(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |. The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.
Ismael
find integration of loge x
Game Reply
find the volume of a solid about the y-axis, x=0, x=1, y=0, y=7+x^3
Godwin Reply
how does this work
Brad Reply
Can calculus give the answers as same as other methods give in basic classes while solving the numericals?
Cosmos Reply
log tan (x/4+x/2)
Rohan
please answer
Rohan
y=(x^2 + 3x).(eipix)
Claudia
is this a answer
Ismael
A Function F(X)=Sinx+cosx is odd or even?
WIZARD Reply
neither
David
Neither
Lovuyiso
f(x)=1/1+x^2 |=[-3,1]
Yuliana Reply
apa itu?
fauzi
determine the area of the region enclosed by x²+y=1,2x-y+4=0
Gerald Reply
Hi
MP
Hi too
Vic
hello please anyone with calculus PDF should share
Adegoke
Which kind of pdf do you want bro?
Aftab
hi
Abdul
can I get calculus in pdf
Abdul
explain for me
Usman
okay I have such documents
Fitzgerald
please share it
Hamza
Practice Key Terms 7

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Source:  OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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