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(2)

(2)

a) y =2f(x - 2) b) y = -f(1/2x)

c) y = f(-x) + 4 d) y = f(-2x - 6)

Total Marks: _____/49 Name: __________

Math 40S Test - Transformations 2011

1. The graph of y = f(x) is shown. Sketch the graphs of thefollowing functions and graphs. Label the new positions

of A and B on your new graphs.

(2)

(2)

___(8)

A(-3, 2)

B(1, -2)

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e) y = | f(x) | f) the inverse of f(x)

g) y = h) Is f(x) a one-to-one function? Explain youranswer.

1

f(x)

i) Write f(x) as a piecewise function.

(2)

(2)

(1)

___(9)

(2)

(2)

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(2)

(2)

(2)

(2)

(2)

___(10)

2. A partial graph of f(x) is drawn below.

a) Complete the graph if f(x) is even. b) Complete the graph if f(x) is odd.

4. The graph of f(x) = x2 is compressed horizontally so that it is 2 times skinnier, reflected in the

y-axis, and translated 3 units upward and 1 to the right. Write the equation of the transformed func-

tion. Do not simplify the equation.

5. Given f(x) has two zeroes: 3 and 12

a) determine the zeroes of y = f(3x) b) determine the zeroes of y = -1

2f(x)

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___(12)

6. Graph the equation y = |(x - 2)3| in 3 steps. Give the equation of each step.

y = |(x - 2)3|a) b)(1) (1)

c) What is the range of y = |(x - 2)3| ? (2)

c) What is the y-intercept of y = |(x - 2)3| ? (2)

(2

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8.

a)Showhowyouwoulddrawthegraphof

Labelallasymptotes.Put"dots"onimportantpoints.Doitinasmanystepsasyouneed.

b)Whatisthedomainandrangeofthefinalfunction?(2marks

)

(8marks)

___10

1

3

1

1

3

y

x

=

+

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BONUS: Graph if f(x) is the piece-wise function, f(x) =1

3( ) 2

yf x

= +

2 2 , 0

4 , 2

x if x

i f x