Note: I believe the answers are the second and third option, I just need validation.

Cupcake Mar 30, 2019

#1**+2 **

Cupcake, put your graph into the desmos program like I did with theother one and then you can see for yourself.

https://www.desmos.com/calculator

I suppose you should work it out first and then use desmos for checking your answer.

Melody Mar 30, 2019

#3**+1 **

https://www.desmos.com/calculator/kwk7kktciz

The green ones do not cross so they are asymptotes.

The orange ones do cross so they aren't

**So do you want to try again?**

(next time maybe you could give me a link to your desmost graph )

Melody Mar 30, 2019

#7**+2 **

Lets look at this anyway. You should not rely on desmos, that is just for checking.

**FIRST WAY (The most formal way)**

\(y=3cot(0.5x)-4\)

The 4 only pushed the graph up or down so it has nothing to do with aspymptotes.

The 3 just exaggerates the graph in a up down direction so that has nothing to do with it either.

so that asymptotes will be the same as for

\(y=cot(0.5x)\)

now

\(y=cot(0.5x)=\frac{cos(0.5x)}{sin(0.5x)}\\ \text{You cannot divide by 0 so the asymptotes will be where sin(0.5x)=0}\\ 0.5x\ne n\pi \qquad where \;n\;is\;an\;integer\\ so\\ x\ne 2n\pi \)

so x canot be 0 or pi or -pi they are three of the asymptotes.

Melody Mar 30, 2019