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Elena L [17]
3 years ago
11

Given the function P(x)=(x-1)^2 write the new function with a Dilation of 2 On THE X

Mathematics
1 answer:
yaroslaw [1]3 years ago
3 0

Answer: New function is y=2(x-1)^2.

Step-by-step explanation:

  • A dilation is a transformation that creates an image using a scale factor that has the exactly same shape as the original, but have a different size.

The given function : P(x)=(x-1)^2

We know that any function y= f(x) will become y=k f(x) after dilation of k units on the x, where k= scale factor for dilation.

Here, the given scale factor = 2 i.e. k=2

Then, the new function will be :

2P(x)=2(x-1)^2

Hence, the new function is y=2(x-1)^2.

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2 years ago
which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1​
lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. y=\sec x

B. y= \tan x

C. y= \cot x

D. y= \csc x

Answer:

A. y=\sec x

D. y=\csc x

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: y=\sec x

We know that, the \sec x=\frac{1}{\cos x}

The range of \cos x is from -1 to 1 given as [-1, 1]. So,

|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1

Therefore, on removing the absolute sign, we rewrite the secant function as:

\sec x\leq -1\ or\ \sec x\geq 1\\

Therefore, the range of y=\sec x is all real numbers greater than or equal to 1 or less than or equal to-1​.

Choice B: y= \tan x

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: y= \cot x

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: y=\csc x

We know that, the \csc x=\frac{1}{\sin x}

The range of \sin x is from -1 to 1 given as [-1, 1]. So,

|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

\csc x\leq -1\ or\ \csc x\geq 1\\

Therefore, the range of y=\csc x is all real numbers greater than or equal to 1 or less than or equal to-1​.

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Step-by-step explanation:

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