Too Easy: To Produce The Graph Of The Function Y=0.5cot(0.5x)

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)? We have prepared the options and answers on this subject for you. Here you go, let’s examine it together.

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To produce the graph of the function Y=0.5cot(0.5x)

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) a horizontal compression to produce a period of pi/2 and a vertical compression
b) a horizontal compression to produce a period of pi/2 and a vertical stretch
c) a horizontal stretch to produce a period of 2pi and a vertical compression
d) a horizontal stretch to produce a period of 2pi and a vertical stretch

To produce the graph of the function Y=0.5cot(0.5x)
To produce the graph of the function Y=0.5cos(0.5x) — **To produce the graph of the function Y=0.5cot(0.5x)**

Answer

C. A horizontal stretch to produce a period of $2\pi$ Pin and a vertical compression.

Step-by-step explanation:

We are given the parent function as $y= \cot x$ Pin

It is given that, transformations are applied to the parent function in order to obtain the function $y=0.5\cot (0.5x)$ Pin i.e. $y=(1)/(2)\cot ((x)/(2))$ Pin

That is, we see that,

The parent function $y= \cot x$ Pin is stretched horizontally by the factor of Pin which gives the function $y=\cot ((x)/(2))$ Pin.

Further, the function is compressed vertically by the factor of Pin which gives the function $y=(1)/(2)\cot ((x)/(2))$ Pin.

Now, we know,

If a function f(x) has period P, then the function cf(bx) will have period Pin.

Since, the period of $y= \cot x$ Pin is $\pi$ Pin, so the period of $y=(1)/(2)\cot ((x)/(2))$ Pin is $(\pi)/(1/2)$ Pin = $2\pi$ Pin

We get option C is correct. That’s it to produce the graph of the function Y=0.5cot(0.5x). We hope you understand. We wish you pleasant work.

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