DP IB Maths: AA SL

Topic Questions

2.5 Transformations of Graphs

1
Sme Calculator
4 marks

The point P left parenthesis negative 1 comma 4 right parenthesis space lies on the curve with equation space y equals straight f left parenthesis x right parenthesis. space

State the coordinates of the image of point P on the curves with the following equations:

(i)

y equals straight f left parenthesis x right parenthesis plus 3

(ii)

y equals straight f left parenthesis x plus 3 right parenthesis

(iii)

y equals 3 straight f left parenthesis x right parenthesis

(iv)
y equals straight f left parenthesis 3 x right parenthesis space

Did this page help you?

2
Sme Calculator
2 marks

The point P left parenthesis negative 3 comma negative 4 right parenthesis lies on the curve with equation y equals straight f left parenthesis x right parenthesis. space.  

State the coordinates of the image of point P on the curves with the following equations:

(i)
y equals straight f left parenthesis negative x right parenthesis
(ii)
space y equals negative straight f left parenthesis x right parenthesis

Did this page help you?

3
Sme Calculator
4 marks

The point P left parenthesis 3 comma 2 right parenthesis space lies on the curve with equation space y equals straight f left parenthesis x right parenthesis.

(i)
On the graph of y equals straight f left parenthesis x right parenthesis plus a, where a spaceis a constant, the point P is mapped to the point left parenthesis 3 comma negative 5 right parenthesis.  Determine the value of  a.

(ii)
On the graph of y equals straight f left parenthesis x plus b right parenthesis, where b spaceis a constant, the point P is mapped to the point left parenthesis negative 1 comma 2 right parenthesis. space  Determine the value of b.

(iii)
On the graph of space y equals c straight f left parenthesis x right parenthesis comma, where c spaceis a constant, the point P spaceis mapped to the point space left parenthesis 3 comma 1 right parenthesis.  Determine the value of c.

(iv)
On the graph of y equals straight f left parenthesis d x right parenthesis comma, where d spaceis a constant, the point P is mapped to the point left parenthesis 1 comma 2 right parenthesis.  Determine the value of d.

 

Did this page help you?

4a
Sme Calculator
4 marks

The diagram below shows the graph of y equals straight f left parenthesis x right parenthesis. space spaceThe two marked points A left parenthesis negative 1 comma 5 right parenthesis and B left parenthesis 3 comma negative 3 right parenthesis lie on the graph.

q4-2-9-transformations-of-functions-edexcel-a-level-pure-maths-medium

In separate diagrams, sketch the curves with equation

(i)

space y equals straight f left parenthesis x minus 1 right parenthesis

(ii)
y equals straight f left parenthesis x right parenthesis plus 3

On each diagram, give the coordinates of the images of points A and B under the given transformation.

4b
Sme Calculator
2 marks

On the graph of y equals straight f left parenthesis x plus a right parenthesis the image of one of the two marked points has an  x coordinate of 2.  Find the two possible values of a.

Did this page help you?

5a
Sme Calculator
4 marks

The diagram below shows the graph of y equals straight f left parenthesis x right parenthesis..  The marked point B left parenthesis 4 comma 8 right parenthesis lies on the graph, and the graph meets the origin at the marked point A.

q5a-2-9-transformations-of-functions-edexcel-a-level-pure-maths-medium

In separate diagrams, sketch the curves with equation

(i)

y equals negative straight f left parenthesis x right parenthesis

(ii)
y equals straight f left parenthesis 4 x right parenthesis

On each diagram, give the coordinates of the images of points A and B under the given transformation.

5b
Sme Calculator
2 marks

On the graph of y equals a straight f left parenthesis x right parenthesis the image of one of the two marked points has a y spacecoordinate of 4. Find the value of a.

Did this page help you?

6a
Sme Calculator
6 marks

The diagram below shows the graph of y equals straight f left parenthesis x right parenthesis.  The graph intersects the coordinate axes at the two marked points A left parenthesis 0 comma 6 right parenthesis and B left parenthesis 3 comma 0 right parenthesis.  The graph has two asymptotes as shown, with equations  space y equals fraction numerator space 20 over denominator 3 end fraction   and  x equals 10 over 3

q6a-2-9-transformations-of-functions-edexcel-a-level-pure-maths-medium

In separate diagrams, sketch the curves with equation

(i)         y equals straight f left parenthesis x right parenthesis minus 6

(ii)       space y equals straight f left parenthesis negative x right parenthesis

On each diagram, give the coordinates of the images of points A and B under the given transformation, as well as stating the equations of the transformed asymptotes.

6b
Sme Calculator
2 marks

The graph of y equals straight f left parenthesis x plus a right parenthesis has an asymptote at one of the coordinate axes.  Find the value of a.

Did this page help you?

7
Sme Calculator
3 marks

Describe, in order, a sequence of transformations that maps the graph of y equals straight f left parenthesis x right parenthesis onto the following graphs:

(i)

y equals 3 straight f left parenthesis x plus 2 right parenthesis

(ii)
y equals straight f left parenthesis negative x right parenthesis minus 1

Did this page help you?

8
Sme Calculator
4 marks

Given that straight f left parenthesis x right parenthesis equals 3 x squared minus 2 x find an expression for straight g left parenthesis x right parenthesis, where straight g left parenthesis x right parenthesis is obtained by applying the following sequence of transformations to straight f left parenthesis x right parenthesis.

Translation by open parentheses table row 2 row 0 end table close parentheses

Vertical stretch of scale factor 4

Translation by open parentheses table row 0 row cell negative 3 end cell end table close parentheses

Did this page help you?

9a
Sme Calculator
4 marks
(i)
Sketch the graph of y equals straight p left parenthesis x right parenthesis, where straight p left parenthesis x right parenthesis equals 3 x minus 4.

(ii)
On the same set of axes, sketch the graph of y equals p to the power of negative 1 end exponent left parenthesis x right parenthesis.
Label the coordinates of the points where each graph crosses the coordinate  axes 
      
9b
Sme Calculator
4 marks
(i)

Find an expression for p to the power of negative 1 end exponent left parenthesis x right parenthesis.

(ii)

 Find an expression for 1 over 9 space left square bracket straight p left parenthesis x right parenthesis plus 16 right square bracket.

(iii)
What can you deduce about the sequence of transformations given
by 1 over 9 left square bracket straight p left parenthesis x right parenthesis plus 16 right square bracket ?

Did this page help you?

10a
Sme Calculator
2 marks

The equation y equals straight f left parenthesis x right parenthesis, where straight f left parenthesis x right parenthesis equals left parenthesis x minus a right parenthesis squared, with a greater than 1, is shown below.

q6a-2-10-combinations-of-transformations-a-level-only-edexcel-a-level-pure-maths-medium

The points A spaceand B are the points where the graph intercepts the coordinate axes.

Write down, in terms of a, the coordinates of A spaceand B.

10b
Sme Calculator
3 marks

Sketch the graph of y equals negative straight f left parenthesis negative x right parenthesis, labelling the images of the points A spaceand B stating their coordinates in terms of a.

10c
Sme Calculator
1 mark

Write down the value of a such that the point A is three times as far from the origin as the point B.

Did this page help you?

11
Sme Calculator
3 marks

The function straight f left parenthesis x right parenthesis is to be transformed by a sequence of functions, in the order detailed below:

A horizontal stretch by scale factor 2

A reflection in the x-axis

A translation by open parentheses table row 0 row 2 end table close parentheses

Write down an expression for the combined transformation in terms of straight f left parenthesis x right parenthesis.

Did this page help you?

12a
Sme Calculator
2 marks

The diagram shows the graph of y equals straight f left parenthesis t right parenthesis, where straight f left parenthesis t right parenthesis equals sin space 2 t,0 degree less or equal than x less or equal than 180 degree.

q7a-2-10-combinations-of-transformations-a-level-only-edexcel-a-level-pure-maths-medium

(i)

Write down the maximum value of y when y equals 3 straight f left parenthesis t right parenthesis.

(ii)
Write down the first value of t for which this maximum occurs.
12b
Sme Calculator
2 marks
(i)

Write down the minimum value of  when y equals 5 straight f left parenthesis t plus 30 degree right parenthesis.

(ii)

Write down the first value of t for which this minimum occurs.

12c
Sme Calculator
2 marks

Find, in terms of straight f left parenthesis t right parenthesis, the combination of transformations that would map the graph of y equals straight f left parenthesis t right parenthesis onto the graph of y equals 2 plus sin space t0 degree less or equal than x less or equal than 180 degree .

Did this page help you?

13a
Sme Calculator
1 mark

Let f open parentheses x close parentheses equals 3 x squared plus 18 x plus 27.

Write down the value of f open parentheses negative 3 close parentheses.

13b
Sme Calculator
3 marks

The function f can be written in the form ofspace f open parentheses x close parentheses equals a open parentheses x minus h close parentheses squared plus k.

Find the values of a, h and k.

13c
Sme Calculator
4 marks

The graph of g is obtained from the graph of f by a reflection in the x-axis followed by a translation by the vectoropen parentheses table row 0 row 1 end table close parentheses .

Findspace g left parenthesis x right parenthesis, giving your answer in the form of g open parentheses x close parentheses equals r x squared plus s x plus t.

Did this page help you?