Parallel lines will always be the same distance apart.
This transformation requires us to shift 1 unit left and 4 units down.
Answer:
5=4=3--35-=3
Step-by-step explanation:
Point slope form:
y - y1 = m(x - 1)
m = -4 , x1 = 4, y1 = 1
equation
y - 1 = -4(x - 4)
hope it helps
![\bf \textit{we know the range for }cos\left( \frac{1}{x} \right)\textit{ is }[-1,1]\textit{ therefore} \\\\\\ -1~\ \textless \ ~cos\left( \frac{1}{x} \right)~\ \textless \ ~1\impliedby \textit{multiplying all sides by }x^2 \\\\\\ -1x^2~\ \textless \ ~x^2cos\left( \frac{1}{x} \right)~\ \textless \ ~1x^2\implies -x^2~\ \textless \ ~x^2cos\left( \frac{1}{x} \right)~\ \textless \ ~x^2](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bwe%20know%20the%20range%20for%20%7Dcos%5Cleft%28%20%5Cfrac%7B1%7D%7Bx%7D%20%5Cright%29%5Ctextit%7B%20is%20%7D%5B-1%2C1%5D%5Ctextit%7B%20therefore%7D%0A%5C%5C%5C%5C%5C%5C%0A-1~%5C%20%5Ctextless%20%5C%20~cos%5Cleft%28%20%5Cfrac%7B1%7D%7Bx%7D%20%5Cright%29~%5C%20%5Ctextless%20%5C%20~1%5Cimpliedby%20%5Ctextit%7Bmultiplying%20all%20sides%20by%20%7Dx%5E2%0A%5C%5C%5C%5C%5C%5C%0A-1x%5E2~%5C%20%5Ctextless%20%5C%20~x%5E2cos%5Cleft%28%20%5Cfrac%7B1%7D%7Bx%7D%20%5Cright%29~%5C%20%5Ctextless%20%5C%20~1x%5E2%5Cimplies%20-x%5E2~%5C%20%5Ctextless%20%5C%20~x%5E2cos%5Cleft%28%20%5Cfrac%7B1%7D%7Bx%7D%20%5Cright%29~%5C%20%5Ctextless%20%5C%20~x%5E2)
if the limit of -x² goes to "something", and the limit of x² goes to the same "something", if their limit coincide, and yet they're bounding the cosine expression, therefore, since the cosine expression is "sandwiched" between -x² and x², then the cosine expression "squeezes in" that little sliver between both -x² and x², and will inevitably go to the same limit.