[Music] hello and welcome to this lesson on reciprocal functions so we're going to plot a reciprocal function and we're going to begin with y is equal to 4 over X neither your values of x and as the value of x changes so we'll value of y so we begin with x equals not 0.5 so Y is equal to 4 divided by not point 5 and 9 is 8 and the coordinate path is made up of an X and the y value and we now know that X is not 0.5 when y is 8 so we can plot this point the next one y is equal to 4 over 1 Y is equal to 4 you and this coordinate goal that one across and follow-up and we have y is equal to 4 over 2 so y is equal to 2 when x equals 2 and this point goes here y is equal to 4 divided by 4 so Y is equal to 1 when X is equal to 4 then we have Y is equal to 4 over 8 so Y is equal to not point 5 when X is equal to 8 and then we have y is equal to four divided by 10 which is not point four that will go approximately there so now we're going to join these points together to make it smooth curve so by looking at the graph you can see that we curve will never actually touch the y-axis here if you think about why nurses we have y is equal to 4 over X and as X approaches 0 we have y is equal to 4 over 0 or approaches 0 and anything divided by 0 is infinite so it's impossible to draw a graph which goes up to infinity so this is one of the properties of a reciprocal function ok let's try the next one okay you want to try and plot this graph for yourself by part than my video and you can redeem it when you're ready so we have the reciprocal function y is equal to 2 over X and to begin with value of X is negative 4 so Y is equal to 2 divided by negative 4 which is negative not point 5 and that would go approximately here I'm a next one y is equal to 2 divided by the new X which is negative 2 and that is negative 1 so that would go here then we have y is equal to 2 divided by negative 1 which is negative 2 and that will go yeah we can plot that up a coordinate negative 1 and negative 2 then we have y is equal to 2 divided by negative nine point five so y is equal to negative four so we can plot a nap here and now we can move to the positive quadrant where Y is equal to 2 divided by positive not 0.5 so y is equal default so when x equals not 0.5 y is equal to 4 why is equal to 2/1 2y is equal to 2y is equal to 2 divided by 2 so a is equal to 1 and finally Y is equal to 2/4 which is not point 5 now we're going to have to reciprocal curves one nv+ first quadrant and one mb- third quadrant so you can see at this point the value of x will approach infinity the same here wait project negative infinity on these two points will quote positive and negative infinity with why this means the curve will get infinitely close to the axes but never actually touch them okay thank you very much for watching I hope you find that useful thanks again I'm taken