SOLUTION: https://webwork.math.umn.edu/webwork2_files/tmp/umtymp-calculus1-f22//gif/a3934625-e78b-3a87-8152-a122c5b59117___a882495f-86b7-3beb-af6b-bbdfd3bcda19.png This is a graph of a ta

Algebra ->  Trigonometry-basics -> SOLUTION: https://webwork.math.umn.edu/webwork2_files/tmp/umtymp-calculus1-f22//gif/a3934625-e78b-3a87-8152-a122c5b59117___a882495f-86b7-3beb-af6b-bbdfd3bcda19.png This is a graph of a ta      Log On


   

Question 1196052: https://webwork.math.umn.edu/webwork2_files/tmp/umtymp-calculus1-f22//gif/a3934625-e78b-3a87-8152-a122c5b59117___a882495f-86b7-3beb-af6b-bbdfd3bcda19.png
This is a graph of a tan or cot function, can you please help to find the equation to the graph.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
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https://webwork.math.umn.edu/webwork2_files/tmp/umtymp-calculus1-f22//gif/a3934625-e78b-3a87-8152-a122c5b59117___a882495f-86b7-3beb-af6b-bbdfd3bcda19.png
This is a graph of a tan or cot function, can you please help to find the equation to the graph.
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Under the link, I see a plot of cotangent function, with the period of 4 units, 
shifted 1 unit horizontally left and without vertical shift.


Its equation is

    y = f(x) = cotan%28%28pi%2F4%29%2A%28x%2B1%29%29%29.


Factor (x+1) in the argument makes the necessary horizontal shift of 1 unit left.


Factor  pi%2F4 makes the necessary period.

Solved and explained.

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In the Internet, there is free of charge online plotting tool

https://www.desmos.com/calculator

where you can check your own different formulas and see, which of them is/(produces) a correct plot / solution.


In particular, by plotting there the graph of my function, you can convince yourself that my answer is correct.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Again in this problem, the intent of the problem is not clear; there are an infinite number of tangent or cotangent functions that have the graph shown.

But the problem says to find "THE" equation for the graph.

The graph shows the function value equal to 0 and decreasing at x=1, and with a period of 4. For simplicity, I will use the "normal" period of pi to show that there are many tangent and cotangent function with the same graph.

The "basic" tangent or cotangent function decreasing at x=0 is y=cot%28x-pi%2F2%29:

graph%28200%2C100%2C-pi%2F2%2C5pi%2F2%2C-5%2C5%2C1%2F%28tan%28x-pi%2F2%29%29%29

But of course the graph will be the same if the horizontal shift is pi/2 plus any multiple of the period pi -- for example y=cot%28x%2B3pi%2F2%29:

graph%28200%2C100%2C-pi%2F2%2C5pi%2F2%2C-5%2C5%2C1%2F%28tan%28x%2B3pi%2F2%29%29%29

The function could also be seen as a tangent function with a negative argument (in which case no horizontal shift is needed), such as y=tan%28-x%29:

graph%28200%2C100%2C-pi%2F2%2C5pi%2F2%2C-5%2C5%2C%28tan%28-x%29%29%29

And then of course this graph can also be shifted by any multiple of the period to obtain the same graph -- for example, y=tan%28-x%2B2pi%29

graph%28200%2C100%2C-pi%2F2%2C5pi%2F2%2C-5%2C5%2Ctan%28-x%2B2pi%29%29