sketching a certain graph... (1 Viewer)

[xmemee]

hi! could someone please help on this quetsion? i have no clue how to approach it...*sighs in defeat*

consider the function
f(x)= 4-(8/x^2+1)

1)find the intersection coordinates to the axis
2)the asymptotes
3)find stationary pts and determine their nature
4)sketch

Thanks SO MUCH if u can help..thanks!

 

[Alexluby]

How do you want people to post a graph on the net....

 

[firehose]

hi! could someone please help on this quetsion? i have no clue how to approach it...*sighs in defeat*

consider the function
f(x)= 4-(8/x^2+1)

1)find the intersection coordinates to the axis
2)the asymptotes
3)find stationary pts and determine their nature
4)sketch

Thanks SO MUCH if u can help..thanks!

1) Let f(x)=0 to find the x intercepts. ie. solve 4(x^2+1)=8 for x
Simply let x = 0 to find the y intercept.
2) To find vertical asymptote(s), let the denominator =0 (as denominator cannot equal zero). As there is no solution for x^2 = -1 there may not be one.
For non-vertical asymptotes, let x approach +/- infinity, using the limit x approaching infinity. Look up a textbook coz they should tell u how to do that really well.
3) to find stationary points, let find dy/dx and let it equal zero. solve for x, and find subsequent y value(s). to determine their nature, you could describe their slope left and right of the value, or u could find d2y/dx2 and describe if it is a possible horizontal point of inflexion.
4) with the stationary points, inflexions, asymptotes and x/y intercepts, the graph should come out well

 

[xmemee]

1) Let f(x)=0 to find the x intercepts. ie. solve 4(x^2+1)=8 for x
Simply let x = 0 to find the y intercept.
2) To find vertical asymptote(s), let the denominator =0 (as denominator cannot equal zero). As there is no solution for x^2 = -1 there may not be one.
For non-vertical asymptotes, let x approach +/- infinity, using the limit x approaching infinity. Look up a textbook coz they should tell u how to do that really well.
3) to find stationary points, let find dy/dx and let it equal zero. solve for x, and find subsequent y value(s). to determine their nature, you could describe their slope left and right of the value, or u could find d2y/dx2 and describe if it is a possible horizontal point of inflexion.
4) with the stationary points, inflexions, asymptotes and x/y intercepts, the graph should come out well

ah, thanks soooo much for ur help! I think i got the gist now..
thanks again for ur time firehose!

 

[firehose]

hehe no worries

 

[redslert]

try this program if you want to look at graphs "grafeq"