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Name - Chapter 4 - Functions Review 1

1) The document provides examples and questions about functions including: composition of functions, inverse functions, translations, stretches, and reflections of graphs. 2) Questions involve evaluating functions, finding domains and ranges, compositions of functions, inverses of functions, and describing transformations of graphs. 3) Diagrams show graphs that have undergone translations, stretches, and reflections to illustrate different transformations.

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Terence Anquandah
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386 views4 pages

Name - Chapter 4 - Functions Review 1

1) The document provides examples and questions about functions including: composition of functions, inverse functions, translations, stretches, and reflections of graphs. 2) Questions involve evaluating functions, finding domains and ranges, compositions of functions, inverses of functions, and describing transformations of graphs. 3) Diagrams show graphs that have undergone translations, stretches, and reflections to illustrate different transformations.

Uploaded by

Terence Anquandah
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as RTF, PDF, TXT or read online on Scribd
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Name _____________________________________________ Chapter 4 – Functions review

1. Consider f(x) = x 5 .

(a) Find

(i) f(11);

(ii) f(86);

(iii) f(5).
(3)

(b) Find the values of x for which f is undefined.


(2)

(c) Let g(x) = x2. Find (g ° f)(x).


(2)
(Total 7 marks)

x4
2. Let f (x) = , x  − 4 and g (x) = x2, x  .

(a) Find (g ◦ f ) (3).

(b) Find f −1(x).

(c) Write down the domain of f −1.


(Total 6 marks)

3. The functions f and g are defined by f :  3x, g : x  x  2 .

(a) Find an expression for (f  g) (x).

(b) Show that f –l (18) + g–l (18) = 22.


(Total 6 marks)

IB Questionbank Maths SL 1
4. Consider the graph of f shown below.

(a) On the same grid sketch the graph of y = f(–x).


(2)

The following four diagrams show images of f under different transformations.

(b) Complete the following table.

Description of transformation Diagram letter


Horizontal stretch with scale factor
1.5
Maps f to f(x) + 1
(2)

IB Questionbank Maths SL 2
(c) Give a full geometric description of the transformation that gives the image in Diagram A.
(2)
(Total 6 marks)

5. The function f is given by f (x) = 1n ( x  2) . Find the domain of the function.

Working:

Answer:

.....................................................................
.

(Total 4 marks)

6. Let f(x) = 7 – 2x and g(x) = x + 3.

(a) Find (g ° f)(x).


(2)

(b) Write down g–1(x).


(1)

(c) Find (f ° g–1)(5).


(2)
(Total 5 marks)

7. Let f(x) = 3x2. The graph of f is translated 1 unit to the right and 2 units down.
The graph of g is the image of the graph of f after this translation.

(a) Write down the coordinates of the vertex of the graph of g.


(2)

(b) Express g in the form g(x) = 3(x – p)2 + q.


(2)

IB Questionbank Maths SL 3
The graph of h is the reflection of the graph of g in the x-axis.

(c) Write down the coordinates of the vertex of the graph of h.


(2)
(Total 6 marks)

1 3
x  x 2  3x
8. Let f(x) = 3 . Part of the graph of f is shown below.

There is a maximum point at A and a minimum point at B(3, –9).

(a) Find the coordinates of A.


(8)

(b) Write down the coordinates of

(i) the image of B after reflection in the y-axis;

  2
 
(ii) the image of B after translation by the vector  5  ;

(iii) the image of B after reflection in the x-axis followed by a horizontal stretch with
1
scale factor 2 .
(6)
(Total 14 marks)

IB Questionbank Maths SL 4

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