Chapter 4 Graphs And Transformations - Year 1

Question 1

Draw the shape of a quadratic with a positive x^2 coefficient

Answer 1

It starts going down and ends going up

Question 2

Describe the shape of a graph with a negative x^2 coefficient

Answer 2

It starts going up end ends going down

Question 3

Describe the shape of a graph with a positive x^3 coefficient

Answer 3

It starts going up and ends going up with a relapse in the middle

Question 4

Describe the shape of a graph with a negative x^3 coefficient

Answer 4

It starts going down and ends going down

Question 5

Describe the shape of a graph with a positive x^4 coefficient

Answer 5

W shape

Question 6

Describe the shape of a graph with a negative x^4 coefficient

Answer 6

M shape

Question 7

Describe the graph of y=x^2

Answer 7

Question 8

Describe the graph y=x^3

Answer 8

Question 9

Describe the graph y=x^4

Answer 9

A longer y=x^2

Question 10

How do you sketch a graph?

Answer 10

Write shape, roots and y intercept down the side of your page

Work out if the highest power of x will be positive or negative then sketch a general shaoemof the graph next to the word shape
Calculate the roots of the equation (factorise)
Calculate the y intercept

Then draw the graph labelling where the graph cut the x and y axis

Question 11

What do you do in case of a double root?

Answer 11

The graph does a double turn when it gets to the cutting point

Question 12

What happens if there is a triple root?

Answer 12

There will be a point of inflexion

Question 13

How do you sketch a cubic that only has 1 real root?
How do you know if it only has 1 real root?

Answer 13

You know that the cubic only has 1 real root if the equation is given in the form (x+d)(ax^2+bx+c) and the quadratic has a discriminant that is less than 0

Since it only has 1 real root the graph must have a point of inflexion because…

Gubihbdijdosjbvfsojbvrwjivbrwojvrojvnejo v

What is the bump called?

Question 14

How can you work out the equation of a cubic or quartic equation if you are given all the points the graph crosses the x axis?

Answer 14

You say reverse the sign and put it into the factorised form of an equation
Then expand it

Eg x=2 x=3 x=-1
(x-2)(x-3)(x+1).

Question 15

If a question asks you to state the value of a, b and c what may be unique about it and how would you answer?

Answer 15

b may be for the x^2 term but there may be no x^2 term in which case b=0

Question 16

How do you calculate the y intercept?

Answer 16

Make all x values 0
The y intercept will be the value without an x attacked to it

Question 17

What does a quartic with a triple root look like?

Answer 17

It has a point of inflexion

Question 18

What do all reciprocal graphs have in common?

Answer 18

There are graphs in two commons

Question 19

In which sectors will a positive x reciprocal graph be in?

Answer 19

1,3

Question 20

In which sectors will a negative x reciprocal graph be in?

Answer 20

2,4

Question 21

In which sectors will a negative x^2 reciprocal graph be in?

Answer 21

3,4

Question 22

In which sectors will a positive x^2 reciprocal graph be in?

Answer 22

1,2

Question 23

What happens as the numerator (in a reciprocal graph gets) bigger?

Answer 23

The space underneath the graph and above the axis gets larger

The asymtope will never change because of this

Question 24

What is the asymptote?

Answer 24

The line that the graph approaches but never reaches

Question 25

What will the equations of the asymptotes normally be?

Answer 25

x=0
y=0

Question 26

What do we know about the gradient of a cubic and quadratic?

Answer 26

The gradient of the cubic will always be greater than the quadratic

Question 27

Ina reciprocal graph how does the denominator change the graph

Answer 27

Unless it is + or - a number it doesn’t

Graphs with a dominator of 2x and x will be the same if the numerator is the same

Question 28

In a graph what should you always lable

Answer 28

Where it crosses the axis
Draw a dot where the points of insertion are

Question 29

How do you find where two lines intercept?

Answer 29

Solve the equations simultaneously

Question 30

Which axis does a change inside the brackets effect?
What do we expect?

Answer 30

X axis
Do the opposite

Question 31

What axis does a change outside the brackets effect?
What do we expect?

Answer 31

Y
What we expect

Question 32

What do we do for the transformation f(ax)?

Answer 32

Divide all the x axis by a

Question 33

What do we do for the transformation af(x)?

Answer 33

Multiply all the y axis by a

Question 34

4.5/4.7 questions……

Question 35

It the question gives you a maximum point. Then tells you that a transformation of f(x)+k has happened what do you do?

Answer 35

Find the difference between the different co-ordinate points

Question 36

What is the first key tip for drawing graphs?

Answer 36

Sketch the axis of the graphs in a different colour

Question 37

Is:
Sqr x =-2 a real solution
Why?

Answer 37

No

The sqr of x can’t be negative

Question 38

If it tells you to only plot 1 graph what doesn’t matter?

Answer 38

The magnitude. (Relative to other graphs. Only the general shale of the graph matters)