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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.
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(2)
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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.
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(2)
(2)
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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)
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8.
a)Showhowyouwoulddrawthegraphof
Labelallasymptotes.Put"dots"onimportantpoints.Doitinasmanystepsasyouneed.
b)Whatisthedomainandrangeofthefinalfunction?(2marks
)
(8marks)
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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