The range of a secant function is (−∞, −4] ∪ [8, ∞). The equations of two consecutive asymptotes of the function are = −pi and =pi. The function is not a reflection over the x-axis. What is the equation of this secant function? Write the equation and state the parts of the equation. Show/explain how you found the various parts of the equation.


Can someone write this out step by step to the answer? I'd like to try to understand...

 Mar 11, 2022
edited by DFO627  Mar 11, 2022

I used Desmos online graphing calc to aid me.

I know 2 asymtotes are x=-pi and x=pi

I know that secant isthe inverse of cos. 


I am much more familiar with the cos function so I will work out what that muct look like.

It must cross the x axis at -pi and pi    That would be half a wavelength.  So the wavelength will be  4pi


It has a maximum at y=8 and a minimum at y=-4

So just by thinking, or sctching what I already know. I can say that (0,8) and (2pi,-4)  will be the max and min.  

     ** Or they could be (0,-4) and (2pi, 8)  but I will wory about that last.


8--4 = 12  the amplitude of the wave is 6,   The average of 8 and -4 is 2   so  y=2 will be the centre line.


So the cos functions is    y=6cos(x/2) + 2               OR      y=-6cos(x/2)+2


The sec function will be    y=6sec(x/2)+2                  or        y=-6sec(x/2)+2





 Mar 11, 2022


I know you have logged on since I posted this.

A response from you would be appreciated.

 Mar 11, 2022

Dude, I don't have to reply to every post!

DFO627  Mar 12, 2022

DFO627 (DumbFuckOnline627):


Melody is not a dude; she’s a teacher. I’m pretty sure this is not the response Melody was looking for.


You titled you question with “Help me please!!!” and you concluded it with, “Can someone write this out step by step to the answer? I'd like to try to understand...”


Melody spent a fair amount of time answering and explaining the solution to your question. She’d like to know if you understood her solution and explanation. This is reasonable. Most teachers like to know if their presentations and instructions are elevating their students above dumbfuck status.


In this case, it’s a classic example of trying to teach a pig to sing. Trying to teach a pig to sing is a waste of time and always annoys the pig.  As anyone may see the pig was very annoyed and presented as a rude little asshole: “Dude, I don't have to reply to every post!”


It wasn’t a complete waste of time though; others will read this and learn from it.  The readers will learn some math ...and how not to be a rude little asshole.


It’s true; you don't have to reply to every post. It’s also true that you don’t have to be a rude little asshole. But you are what you are: a dumbfuck online and a rude little asshole. You chose that path... you are still young enough to change your path....



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Guest Mar 12, 2022
edited by Guest  Mar 12, 2022

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