Transformations

Transformations

Total   ______    =    _________%

1.    For the function   graphed below. Sketch each function on the grid provided.
For each graph:    a) explain what change(s) you made to  .
b) Give the new coordinates of the point provided in each question.
(4 marks for each, 2 marks for graph)

a)

______________________________________

______________________________________

________________

b)

_______________________________________

_______________________________________

________________

c)

__________________________________

__________________________________

_______________

d)

___________________________________

___________________________________

______________

2.     Given the graph of   , on the same grid sketch the graph of

3 marks

3.    Given the graph of the function   below, sketch the graph of   on the grid provided.

3 marks

4.    Two functions are graphed below.   and   . Determine the values of   and  .

4. ________________________
2 marks
5.    The graph of    is shown below. The sketches of transformations of   are given in the following graphs. Write an equation in terms of   to represent the graphs of the transformations.

a)

a) _____________________
2 marks

b)

b) _____________________
2 marks

c)

c) _____________________
2 marks

6.    Write the equation of the transformed function    after the following transformations
in the order given.

a)  A vertical compression by a factor of  followed by a transformation of 3 units right.

a) ___________________________
2 marks
b)  A horizontal compression by a factor of   , then a reflection in the  -axis followed
by 2 units down.

b) ___________________________
2 marks

c)    A horizontal expansion by a factor of 6 followed by a translation of 4 units left and 5 units up.

c) ___________________________                                                        2 marks
7.    The graph of   has the following transformation applied to it. Determine an
equation for the new graph.

a)  a horizontal compression by a factor of  .

a) ___________________________
2 marks
b) a vertical expansion by a factor of 3, then reflected in the  -axis.

b) ___________________________
2 marks

8.    If  , determine the equation of  , the inverse of  .

8.____________________________
3 marks

9.    For the function   graphed below, list all the coordinates of the invariant points for the
following transformations.

a)
b)
c)

a) ___________________________
2 marks

b) ___________________________
2 marks

c) ___________________________
2 marks

10.    The point   is on the graph of  , which point must be on the graph
of  ?

10. ___________________________                                                                            2 marks

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