C3

Question 1

What is domain of function

Answer 1

x values ↔ e.g -1

Question 2

What is the range of a function

Answer 2

y values ↨ e.g f(x) > -5

Question 3

What is the order for function fg(x)

Answer 3

First g then f = f [ g(x) ]

Question 4

When do functions have an inverse

Answer 4

when f(x) is one-one

Question 5

How do you find inverse equation

Answer 5

1. Rearrange to make x the subject

2. Switch y and x

Question 6

What is the range and domain for inverse functions

Answer 6

Inverse domain= normal range

Inverse range= normal domain

Question 7

How do you solve modulus equations e.g | 9-x^2 |=5

Answer 7

1. First solve equation removing modulus sign

2. Then switch the sign of the modulus parts and solve it again.

Question 8

How do you make modulus graphs on calculator

Answer 8

1. Graph section
2. OPTN
3. Num
4. ABS
5. Brackets around the equations.

Question 9

Describe the inverse graph sin-1(x)

Answer 9

1. domain -1< x <1
2. range -pi/2 < sin^-1(x) < pi/2
3. < should be the same or equal to sign

Question 10

Describe the inverse graph tan^-1(x)

Answer 10

1. domain- all real numbers

2. Range -pi/2 < tan-1(x)

Question 11

Describe the inverse graph cos-1 (x)

Answer 11

1. Domain -1< x <1
2. Range 0< cos^-1(x)< pi
3. < should be the same or equal to sign

Question 12

What is 1/sin(x) and describe the graph

Answer 12

1. cosec(x)
2. The graph is separate curves that start at the points where the sin(x) meet 1 and -1.
3. Asymptotes where sin (x) graph met x-axis

Question 13

What is 1/cos(x) and describe the graph

Answer 13

1. Sec (x)
2. The graph is separate curves that start at the points where the cos(x) meet 1 and -1.
3. Asymptotes where cos (x) graph met x-axis

Question 14

What is 1/tan(x) and describe the graph

Answer 14

1. Cot(x)
2. reflections of the tan(x) graph
3. Look at it as it is hard to describe

Question 15

What is the relationship between e^x and ln(x)

Answer 15

They are inverse functions so cancel each other out

Question 16

Describe the graphs of ln(x) and e^x

Answer 16

1. e^x looks like a graph of any number ^x with an asymptote at y=1
2. ln(x) is the reflection y=x with asymptote at x=1

Question 17

Differentiate e^x

Answer 17

e^x

Question 18

Differentiate e^kx

Answer 18

ke^kx

Question 19

Differentiate ln(x)

Answer 19

1/x

Question 20

What is the circle of differentiation starting with sin(x)

Answer 20

sin(x) → cos(x) → -sin(x) → -cos(x) → sin(x)

Question 21

Differentiate tan(x) and tan(ax)

Answer 21

sec^2(x), asec^2 (ax)

Question 22

Differentiate cot(x) and cot(ax)

Answer 22

-cosec^2(x), -acosec^2(ax)

Question 23

Differentiate sec(x) and sec(ax)

Answer 23

sec(x)tan(x), asec(ax)tan(ax)

Question 24

Differentiate cosec(x) and cosec(ax)

Answer 24

-cosec(x)cot(x), -acosec(ax)cot(ax)

Question 25

Differentiate sin(ax) and cos(ax)

Answer 25

acos(ax), -asin(ax)

Question 26

Differentiate ln(f(x))

Answer 26

f’(x)/ f(x)

Question 27

What are the 3 rules for differentiation

Answer 27

1. Product rule y=uv
2. Quotient rule y=u/v
3. Chain rule, used for composite functions e.g y=(2x+4)^3, y= sin(x+1)

Question 28

Write formula of product rule

Answer 28

dy/dx= u* dv/dx + v*du/dx

Question 29

Write formula of quotient rule

Answer 29

dy/dx= (Vdu/dx - Udv/dx)/V^2

Question 30

Write formula of chain rule

Answer 30

dy/dx= dy/du * du/dx

Question 31

How do you show equation x^3 + x^2 -5 =0 has root between x=1 and x=2

Answer 31

Do f(1) and f(2) and if the sign changes and functions it shows the root is between 1 and 2

Question 32

volume of revolution formula about x axis

Answer 32

Volume= integration( pi*y^2) dx

Question 33

Volume of revolution formula about y axis

Answer 33

Volume= integration( pi*x^2) dy