Graphs & Transformations 5 • Sketching Reciprocal Graphs • P1 Ex4C • 🤖

[@khaalidcarab1403]

i am a homeschooling student and you are my only teacher when i get stuck thanks 💌

[@BicenMaths]

Let me know if you need anything via the comments! :)

[@lotsoflove6182]

Hi Sir, will the asymptotes of a reciprocal graph always be at the x and y axis, regardless of the value of a? And will they expect us to label them?

[@BicenMaths]

If the graph is in the form y=a/x then yes the asymptotes will always be the axes, and yes this should be stated. However, it’s likely they’d ask you to draw a transformation instead eg y=a/x + 1, in which case it shifts up one unit so would have an asymptote at y=1 as well as the y axis.

[@lotsoflove6182]

@@BicenMaths Great, thank you so much sir!!!

[@sanamore6658]

Sir, sorry would you be able to explain why the asymptotes mean that y=0 is the x-axis? I don’t really understand that part.

[@BicenMaths]

So, think of all the coordinates along the x-axis... things like (5, 0) (2, 0) (0, 0) (-3, 0)... all the points on the x-axis have y coordinate 0, so we represent that line as y=0. Hope this helps!

[@bharadwajeddanapudi8507]

Sir, in general, would the shape be different in the 1st quadrant for a '1/x' and '1/(x^2) line?

[@BicenMaths]

The shapes appear the same in the first quadrant, but if you had them both plotted at the same time, you'd see that the 1/x^2 branch looks a little different to the 1/x graph. But from separate sketches they'd look the same! Try it on Desmos.

[@bharadwajeddanapudi8507]

@@BicenMaths Ok will do. Thanks sir

[@GillyBoi100]

Thanks