Advanced functions Isu

Logarithms-increasing/decreasing

100

-logx 

Is this log increasing or decreasing 

Decreasing

200

Logx

Is this function increasing or decreasing 

Increasing 

300

3logx

Is this increasing or decreasing 

Increasing

400

6log(x-3) +5

Increasing or decreasing 

Increasing

500

-4log(x+2)-1 increasing or decreasing 

Decreasing 

Combination of functions

100

F= { (-4,2), (-2,5) , (0,3) (1,4) (2,7) }

G= { (-4,1), (-2,4), (-1,5), (0,4)(2,6)}

Find f+g

F+g= {(-4,3),(-2,9)(0,7),(2,13)}

200

Find f x g

F= { (-4,2), (-2,5) , (0,3) (1,4) (2,7) }

G= { (-4,1), (-2,4), (-1,5), (0,4)(2,6)}

F x g = {(-4,2), (-2,20), (0,12), (2,42) }

300

F(x)=2x+3

G(x)=x²

Find F+g

X² +2x+3

400

F(x)=2x+3

G(x)=x²

Find F-g

-x² +2x+3

500

F(x)= 2x+3

g(x)+ x²

Find Fg

2x³+3x²

Solving limits/ Substitution

100

Solve the limit

limx³

x-->-2

-8

200

lim x+2/x³+8

x-->3

1/7

300

lim x²+3 / 1-x

x->1 

= 4/0

= undefined 

400

lim x-4 / x²-16

x -> 4

= 1/8

500

lim sqaure root of (x+3) - 2 / x-1

x-> 1

1/4

Solving quadratic trig equations

100

sin²x - sinx = 2

sinx x = 2, no solution

sinx = 1, x = 3pi / 2

200

2cos²x - 3cosx + 1 = 0

cosx = 1, x = 2pi, x = 0 

cosx = 1/2, Q1: x = pi/3, Q4: x = 5pi/3

300

sin²x +sinx = cos²x

sinx = 1/2, Q1: pi/6, Q2: 5pi/6

sinx = -1, x=3pi/2

400

5(2cos²x -1) - cosx + 3 = 0

cosx = 1/2, Q1: x=pi/3, Q4: x = 5pi/3

cosx = -2/5, Q2: x=1.98, Q3: x=4.3

500

sin²x - cos²x -3sinx + 2 = 0

sinx = 1, x=pi/2

sinx = 1/2, Q1: x= pi/6, Q2: x= 5pi/6

Difference of squares

100

x²-100

=(x-10)(x+10)

200

4x²-9

(2x-3)(2x+3)

300

x⁴-y²

=(x²-y)(x²+y)

400

25x²-9y²

=(5x-3y)(5x+3y)

500

8x²-18y⁴

=2 [ (2x-3y²)(2x+3y²)]