Functions... (1 Viewer)

[Smile12345]

How do you find...

f(3) - f(-1) if:

f(x) = x2 (x squared) + 1 when x is greater than or equal to 2
= 3x - 5 when x is less than 2

By the way, is there any symbols I could use to make this clearer somewhere??

Thanks heaps...

 

[yasminee96]

find f(3) and f(-1) separately, taking the conditions into account, and then subtract.
considering 3>2, therefore you will use f(x)=x^2 +1 as this function applies for all values greater than or equal to 2
so f(3) = 3^2 + 1 = 10
considering -1<2, thus you will use f(x)=3x-5 as this applies for all values less than 2
so f(-1) = 3(-1) -5 = -8

now bring them together,
f(3)-f(-1)= 10 - (-8) = 18


hope this helped

 

[Smile12345]

Thanks heaps....

If I had to draw a neat sketch for y=x^2 + 4x -12..... The x intercepts would be 2 and -6 wouldn't they? And the y intercept (when x = 0) would be -12?

Is this correct?

 

[yasminee96]

i believe the x-intercepts would be -2 and 6
because the "template" is x^2 + (sum of roots)x + (product of roots)
in this case your sum is +4, so -6 +2 would give -4, to get +4 you need -2+6

y-intercept is correct

 

[Smile12345]

Thanks for your help...

I thought that y = x^2 (x squared) + 4x -12 could be put into two sets of brackets (x-2)(x+6) then to get the to x ints: x-2=0 so x=2, then x+6=0 so x= -6... Is this right?

 

[HeroicPandas]

i believe the x-intercepts would be -2 and 6
because the "template" is x^2 - (sum of roots)x + (product of roots)
in this case your sum is +4, so -6 +2 would give -4, to get +4 you need -2+6

y-intercept is correct

Quadratic = x^2 - (sum of roots)x + (product of roots) (remember ur minus!)

Thanks for your help...

I thought that y = x^2 (x squared) + 4x -12 could be put into two sets of brackets (x-2)(x+6) then to get the to x ints: x-2=0 so x=2, then x+6=0 so x= -6... Is this right?

u are absolutely correct, nothing beats factorisation

 

[Smile12345]

Thanks for confirmation 'HeriocPandas'

Could you help me with...
Sketch region defined by: x^2 + y^2 less than or equal to 4, and y less than x....

For a start, I know the first equation is a circle coloured in but what kind of equation is y less than x?

Also... If I have the points A(2,4) B(5,-2) and C(1,-1) As vertices of a triangle... How do I find the coordinates of D when 'A line is drawn through C to meet AB at right angles at the point D'??

Thanks

 

[HeroicPandas]

u done the circle part



y<x, y = x is a line satisfying (0,0) (1,1) (2,2) (3,3), etc

y<x so shade the bottom (using the vertical line test - draw vertical line on the curve, since less than, we choose the bottom)

NB: its less than but NOT EQUAL TO, hence the line y = x must be dotted

2) Let D be (x,y)

'line drawn through C meet AB at right angles at point D'

so u want to find this line (let this line be line L)

1. Identify that point C will pass through the line L
2. Find gradient of AB
3. Identify that line L has gradient perpendicular to line AB
4. Find it using m1.m2 = -1
5. Laugh as u have found the line L using the 'one-point gradient formula'
6. Solve simultaneously line L and line AB to find point D


goodluck and also, i try to not give u false information, but i dont have the time to fully write up a full solution (so all this is to the best of my ability worked mentally)

EDIT: something happened to this.... first part of my message is hidden for some reason - to view it, click 'REPLY TO QUOTE' and read what i typed

 

[Smile12345]

Thanks for your help...Yes I got the first part of your message....

I'll just go through '2' now.... No worries that's fine, I can understand. Thanks for taking as much time as you have....

I've got my 1/2 Yearly Exam next week... Any tips?

 

[HeroicPandas]

Thanks for your help...Yes I got the first part of your message....

I'll just go through '2' now.... No worries that's fine, I can understand. Thanks for taking as much time as you have....

I've got my 1/2 Yearly Exam next week... Any tips?

-dont be afraid
-try to concetrate a lot while ur studying, some teachers say 'ur performance in ur test reflects how much u study and how u study'. So if u concentrate and do practice questions just like if they were in the test (TO THE BEST OF UR ABILITY), u'll do fine
-logic is ur best friend
-dont go insane and do 1000 questions
-what u are provided in maths, u go find it (perfect example of this is question '2' - i found the line and then the rest i can predict)
-everyone has different exam techniques such as skipping a question if u take a while to do it (i did this and forgot about it ahha), develop ur own "style"
-conclusively, goodluck, be sure to concentrate when ur studying, in my opinion, if u dont FULLY concentrate while studying, u wont reach ur potential

 

[Smile12345]

Thanks for that! It is my favourite subject....

Sorry, I'm not just quite clear on 2 ... What was the equation for line L so I can do the simultaneous equations?? Is it y=1/2x then what?

 

[HeroicPandas]

Thanks for that! It is my favourite subject....

Sorry, I'm not just quite clear on 2 ... What was the equation for line L so I can do the simultaneous equations?? Is it y=1/2x then what?

i told u what do...

 

[HeroicPandas]

Line L passes through C (1,-1)

Using one-point gradient formula or w/e u want to call it:



Find line AB using 2-point gradient formula:



Then solve simultaneously line AB and L to obtain point D

 

[Smile12345]

Stuff I'm dumb... Thanks heaps... You even said to use the one point gradient formula!!

 

[HeroicPandas]

Stuff I'm dumb... Thanks heaps... You even said to use the one point gradient formula!!

u arent dumb, u just need more practice to see the beauty of maths. Having a gloomy mentality is not good, it makes u worse as i've experienced it last year

remember to use all the information given in the question and NEVER BACK DOWN!

 

[Smile12345]

u arent dumb, u just need more practice to see the beauty of maths. Having a gloomy mentality is not good, it makes u worse as i've experienced it last year

remember to use all the information given in the question and NEVER BACK DOWN!

Now that is true. I just need more practice and really enjoy the beauty of maths - basically because it's logic. I agree, it makes it worse.

Thanks, I will do that!! I am determined to move up in the rankings anyway... I have another question...

How do you make attachments?