yr11 3U maths questions (1 Viewer)

[Awesomeness...]

Hi all
i have my half yearlies next week and i stumbled across some questions i need help with

Solve 5m+4/2m < 1/4

Sketch y=3/x^2-4

 

[ratcher0071]

Sketch y=3/x^2-4

For this:
-find asymptotes (vertical)
-find the y-intercept (let x=0)
-think about domains x < -2 , -2 < x <2 , x > 2
-end of curves approaches the aysmptotes

Solve 5m+4/2m < 1/4

For this:
-multiply both sides by the square of the denominator (i.e. (2m)²)
-re-arrange, do not cancel 2m from the numerator on both sides!
-factorise and solve for m
-should get .... < m < .....

 

[Awesomeness...]

For this:
-multiply both sides by the square of the denominator (i.e. (2m)²)
-re-arrange, do not cancel 2m from the numerator on both sides!
-factorise and solve for m
-should get .... < m < .....

i did this and it didnt work >.<

i have another question,
if f(x) = 2ax+b, find the values of a and b given that f(-1)=5 and f(2)=-1

 

[gurmies]

f(x) = 2ax + b

f(-1) = 5

b - 2a = 5 [1]

f(2) = -1

4a + b = -1 [2]

[2]-[1] yields 6a = -6

a = -1

.'. b = 3

 

[jchoi]

The sketch part is simple, you draw:
y=3/x^2-4, u put under simple denominator, draw the reciprocal graph of this, then once again, draw reciprocal of that. Or, you can use calculus, find s.p/p.o.i and its natures, the see when x-> infinite.

 

[gurmies]

The sketch part is simple, you draw:
y=3/x^2-4, u put under simple denominator, draw the reciprocal graph of this, then once again, draw reciprocal of that. Or, you can use calculus, find s.p/p.o.i and its natures, the see when x-> infinite.

 

[jchoi]

wat did u draw this graph on?

 

[khorne]

First, factorise
Find vertical asymptotes ( at denominator = 0)
Find horizontal asymptotes (as x-> infinity)
Find x,y intercepts
Taken that this form of function can only change signs at discontinuities and 0's (x intercepts) find the behavious of the function near the asymptotes and at the 0's (eg, from which direction/sign does the function approach from?)

Otherwise, you could use first/second derivative, but idk if you've learnt that