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What are the key characteristics of the graph of f(x)=csc x?

Select all correct statements.

1.The y-intercept is (0,1).

2.The range of the function is (−∞, −1]∪[1, ∞) .

3.The x-intercepts occur every π, with one x-intercept at (π2,0).

4 .Asymptotes occurs every π, beginning at x = 0.

 Feb 21, 2020
 #1
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Look  at the graph here   :   https://www.desmos.com/calculator/a6sxjsqyr4

 

Note that

 

There is no y intercept.....so  (1)  is false

 

From the graph....(2)  is true

 

There are no x intercepts.....(3)  is false

 

The last is true........csc  = r /y  .....    at   0  + n*pi    where n  is an integer,  y  = 0....and since we can't divide by  0, the  csc is not defined at these  values

 

 

cool cool cool

 Feb 21, 2020

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