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# Sketching functions help please! watch

1. Would some please explain a step by step procedure to sketching graphs? Without calculus. I know i have to find the domain, poles and zeroes,(i know how to find the former three), and all its asymptotes.
But Im not quite sure how to tackle the way in which the functions changes...and how to tell how the function behave ( as in which direction its heading towards). When its at its min point etc. Or when the function splits.

Please explain how to do so! It would be greatly appreciated!
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2. Exercise 2.pdf (91.7 KB, 98 views)
3. (Original post by Trufflezz)
Would some please explain a step by step procedure to sketching graphs? Without calculus. I know i have to find the domain, poles and zeroes,(i know how to find the former three), and all its asymptotes.
But Im not quite sure how to tackle the way in which the functions changes...and how to tell how the function behave ( as in which direction its heading towards). When its at its min point etc. Or when the function splits.

Please explain how to do so! It would be greatly appreciated!
Solve f(x)=0 to find roots (where graph crosses x axis)

Set x to 0 to find where graph crosses y axis.

Differentiate function, set f'(x)=0 for turning points

Differentiate again f''(x) to find nature of turning points.

If second derivative >0 SP is minimum

If second derivative <0 SP is maximum

If second derivative = 0, point of inflexion.

I know you said no calculus.. So you could complete the square on the function to find the info, however not always possible/easy to complete the square.

Hope that helped.

SP is turning point or stationary point
4. (Original post by Trufflezz)
Would some please explain a step by step procedure to sketching graphs? Without calculus. I know i have to find the domain, poles and zeroes,(i know how to find the former three), and all its asymptotes.
But Im not quite sure how to tackle the way in which the functions changes...and how to tell how the function behave ( as in which direction its heading towards). When its at its min point etc. Or when the function splits.

Please explain how to do so! It would be greatly appreciated!
Since you have said that you do not want to use calculus here's a simple option.

For many of your questions it will be helpful to factorise. Having done that you can consider the signs of the factors in various intervals.

Why not chose one of your eleven questions to work through and get some help with?
5. (Original post by BuryMathsTutor)
Since you have said that you do not want to use calculus here's a simple option.

For many of your questions it will be helpful to factorise. Having done that you can consider the signs of the factors in various intervals.

Why not chose one of your eleven questions to work through and get some help with?
can u help me out with question (b) and (f)? Please? Thanks a bunch!
6. (Original post by Trufflezz)
can u help me out with question (b) and (f)? Please? Thanks a bunch!
Yes. Were you able to apply my hints to (b)? What did you get?
7. (Original post by BuryMathsTutor)
Yes. Were you able to apply my hints to (b)? What did you get?

negative in the first interval, positive in the 2nd and 3rd, negative in the fourth?

I plugged in x values in those intervals and plotted them...its that how i was suppose to do it?

or is there a quicker way?
8. fpr ppart (f) i dnt even know how to start...its such an ugly function ...
9. (Original post by Trufflezz)
fpr ppart (f) i dnt even know how to start...its such an ugly function ...
factorise the numerator in terms of .. (then cancel down)

simplifies to: (verify this!):

so it`s not really that ugly...
10. (Original post by ApplyYourself)
Solve f(x)=0 to find roots (where graph crosses x axis)

Set x to 0 to find where graph crosses y axis.

Differentiate function, set f'(x)=0 for turning points

Differentiate again f''(x) to find nature of turning points.

If second derivative >0 SP is minimum

If second derivative <0 SP is maximum

If second derivative = 0, point of inflexion.

I know you said no calculus.. So you could complete the square on the function to find the info, however not always possible/easy to complete the square.

Hope that helped.

SP is turning point or stationary point
Not necessarily. Consider given by .
11. (Original post by poorform)
Not necessarily. Consider given by .
Yeah, C2 that's what I was told (point of inflexion) ... I blame the books
12. (Original post by ApplyYourself)
Yeah, C2 that's what I was told (point of inflexion) ... I blame the books
It can be a point of inflexion but it doesn't have to be as my example shows. To be honest if then you could either use the first derivative test or compare both above and below to see if the concavity has changed.
13. f) is kinda difficult to do without some form of calculus - limits essentially.

the fuction you end up with is:

which approaches as approaxhes from the left - (this is a {global} minimum point)

and approaches as approaches from the right

then what does y approach (easy this) as x approaches +/- infinity?...

(also, there is a point of inflection below x=-1, but without calculus....)

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