To produce the graph of the function y = 0.5cot(0.5x), what transformations should be applied to the

8 answers
Question:

To produce the graph of the function y = 0.5cot(0.5x), what transformations should be applied to the graph of the parent function Y = cot(x)?
a horizontal compression to produce a period of and a vertical compression
a horizontal compression to produce a period of î and a vertical stretch
a horizontal stretch to produce a period of 27 and a vertical compression
a horizontal stretch to produce a period of 2x and a vertical stretch

Answers

answer: suck one

step-by-step explanation: suck one

C if not D .

Step-by-step explanation:

EDG 2020

C. A horizontal stretch to produce a period of [tex]2\pi[/tex] and a vertical compression.

Step-by-step explanation:

We are given the parent function as [tex]y= \cot x[/tex]

It is given that, transformations are applied to the parent function in order to obtain the function [tex]y=0.5\cot (0.5x)[/tex] i.e. [tex]y=\frac{1}{2}\cot (\frac{x}{2})[/tex]

That is, we see that,

The parent function [tex]y= \cot x[/tex] is stretched horizontally by the factor of [tex]\frac{1}{2}[/tex] which gives the function [tex]y=\cot (\frac{x}{2})[/tex].

Further, the function is compressed vertically by the factor of [tex]\frac{1}{2}[/tex] which gives the function [tex]y=\frac{1}{2}\cot (\frac{x}{2})[/tex].

Now, we know,

If a function f(x) has period P, then the function cf(bx) will have period [tex]\frac{P}{|b|}[/tex].

Since, the period of [tex]y= \cot x[/tex] is [tex]\pi[/tex], so the period of [tex]y=\frac{1}{2}\cot (\frac{x}{2})[/tex] is [tex]\frac{\pi}{1/2}[/tex] = [tex]2\pi[/tex]

Hence, we get option C is correct.

D

Step-by-step explanation:

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Step-by-step explanation:

The correct answer is the first one.

Step-by-step explanation:

Let's analyse the effect of each modification in the function.

The value 6 multiplying the cot function means a vertical stretch.

The value of 3 multiplying the x inside the function is a horizontal compression, which causes the period to be 3 times lower the original period.

The original period of the cotangent function is pi, so the horizontal compression will make the period be pi/3.

The value of -pi/2 inside the cotangent function normally causes a horizontal shift of pi/2 to the right, but the x-values were compressed by a factor of 3 (horizontal stretch), so the horizontal shift will be 3 times lower: (pi/2) /3 = pi/6

And the value of 4 summing the whole equation is a vertical shift of 4 units up.

So the correct answer is the first one.

CorrectThe direction of the electric field stays the same regardless of the sign of the charges that are free to move in theconductor.Mathematically, you can see that this must be true since the expression you derived for the electric field isindependent of .Physically, this is because the force due to the magnetic field changes sign as well and causes positive charges tomove in the direction (as opposed to pushing negative charges in the direction). Therefore the result isalways the same: positive charges on the side and negative charges on the side. Because the electric fieldgoes from positive to negative charges will always point in the direction (given the original directions of

Given the graph of [tex]y=\cot x[/tex], horizontally stretching the graph by a factor of 3 (i.e. reducing the period of the graph or increasing the number of turns in a given interval by a factor of 3) gives the graph [tex]y=\cot3x[/tex].

Now, shifting the graph by [tex]\frac{\pi}{2}[/tex] units to the right gives the graph of [tex]y=\cot\left(3x- \frac{\pi}{2} \right)[/tex] and vertically stretching the graph by a factor of 6 (i.e. increasing the height of each point on the graph by a factor of 6 relative to the original position) gives the graph of [tex]y=6\cot\left(3x- \frac{\pi}{2} \right)[/tex]

Finally, shifting the graph by 4 units up gives the graph of [tex]y=6\cot\left(3x- \frac{\pi}{2} \right)+4[/tex]

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