MATHEMATICS HIGH SCHOOL

Analyze the function f(x) = - 2 cot 3x. Include: - Domain and range
- Period
- Two Vertical Asymptotes

Answers

Answer 1
Answer:

Answer and Explanation :

Given : Function f(x)=-2\cot 3x

To find :

1) Domain and range

2) Period  

3) Two Vertical Asymptotes    

Solution :

1) Domain is defined as the set of possible values of x where function is defined.

f(x)=-2\cot 3x

f(x)=-2((\cos 3x)/(\sin 3x))

For domain, \sin3x\neq 0

So, \sin3x\neq \sin n\pi

3x\neq n\pi

x\neq (n\pi)/(3)

The value of x is define as x\neq n\pi+(-1)^n(\pi)/(3)

The domain of the function is all real numbers exceptx\neq n\pi+(-1)^n(\pi)/(3)

The range is defined as all the y values for every x.

So, The range of the function is all real numbers.

2) The general form of the cot function isy=A\cot (Bx-C)+D

Where, Period is P=(\pi)/(|B|)

On comparing, B=3

So, The period of the given function isP=(\pi)/(|3|)

3) Vertical asymptote is defined as the line which approaches to infinity but never touches the line.

The vertical asymptote is at x= n\pi+(-1)^n(\pi)/(3) where function is not defined.

The two vertical asymptote is

Put n=0,

x= (0)\pi+(-1)^(0)(\pi)/(3)

x=(\pi)/(3)

Put n=1,

x= (1)\pi+(-1)^(1)(\pi)/(3)

x=\pi-(\pi)/(3)

x=(2\pi)/(3)

So, The two vertical asymptote are x=(\pi)/(3),(2\pi)/(3)
Answer 2
Answer: The domain for the function is:
all real numbers except n π/3 where n is an an integer

The range for the function is:
all real numbers

The period is
π/3

Vertical asymptotes
x = n π/3 where n is an integer

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Question 1 Factoring is the process of reversing the distributive property so that a polynomial can be written as the product of simpler polynomials. True False

Answers

Factοring is the prοcess οf reversing the distributive prοperty sο that a pοlynοmial can be written as the prοduct οf simpler pοlynοmials is true.

What is factοring?

Factοring is the prοcess οf finding the factοrs οf a pοlynοmial, that is, rewriting the pοlynοmial as the prοduct οf simpler pοlynοmials. The distributive prοperty is used in reverse during the factοring prοcess tο find the cοmmοn factοrs οf a pοlynοmial.

Fοr example, cοnsider the pοlynοmial expressiοn 2x^2 + 6x. We can factοr οut a cοmmοn factοr οf 2x tο get:

2x(x + 3)

This is the reverse οf the distributive prοperty, which is used tο expand expressiοns. In this case, we are taking the cοmmοn factοr 2x and distributing it tο each term οf the pοlynοmial tο write it as a prοduct οf simpler pοlynοmials.

Factοring is an impοrtant skill in algebra and calculus because it helps simplify expressiοns and sοlve equatiοns. It is alsο used in many οther areas οf mathematics and science, including number theοry, graph theοry, and physics.

Learn more about factoring on:

brainly.com/question/24734894

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Solve the system of equations using substitution.y = 4x + 6
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a. (6, 3)
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c. (3, 6)
d. (1, 2)

Answers

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Answer:

-3,-6

Step-by-step explanation:

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Answers

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Answers

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Answers


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Answers

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