Transformations of Functions Quiz Name ______________________Integrated Math 2 Date ___________ Block: _____

You have 40 minutes. Calculators are not permitted.

1) Find the image equation of the following functions after applying the given transformations:

a) after a vertical translation 3 units up 1 mark – K

b) after a reflection around the x-axis 1 mark – K

c) after a vertical dilation by a factor of 4 1 mark – K

2) The graph of f (x) is pictured below. On the same axes, graph the following transformations of f (x). Clearly label your different functions!!

a) f ( x)

3 marks – A

b) f (x + 2) – 5 3 marks – A

c) f (-x) 2 marks – A

3. e) Describe the transformations, in words, that occur in going from

i) f (x) to a)_______________________________________________________ 1 K, 1 C

ii) a) to b)_________________________________________________________ 1 K, 1 C

iii) b) to c)_________________________________________________________ 1 K, 1 C

iv) c) to d)_________________________________________________________ 1 K, 1 C

1 K

1 K

1 K

1 K

Note, each equation will build on the previous equation, until your final equation is in the form

- it is possible

that not all a, b, c, d will be used.

4) Julie graphed a transformation from f (x) = x2 and Jen graphed a transformation from f (x) = x2

to like this: to like this:

Even though both students graphed a vertical shift up 3 units, and a vertical reflection around the x-axis, their final results look different. Explain (with some specifics) why this is the case. Whose results are correct?

4 marks – T

5) Since Richard knows about transformations, he can make informed predictions about functions and their characteristics and their properties. For example, given the function y = – (x + 3)2 – 6, he can make a prediction (just by looking at the function) as to:

(a) whether or not the parabola opens upwards or downwards.

(b) whether or not the parabola has x-intercepts.

So, does the function: (a) open up or down? How do you know?

So, does the function: (b) have x-intercepts? How do you know?

2 marks – T2 marks – C

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Totals: Application: /8 Communication/Technology: /6

Knowledge: /11 Critical Thinking: /6