bergmath.files.wordpress.com · Web viewSep 02, 2017 · Station 1- Describing compositions of...
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Station 1- Describing compositions of functions given the function.
Check in!
1. Let f ( x )=2−x2 and g ( x )=x2−2.Explain the differences in the transformations each of these functions went under from the parent function, x2.
2. For the graph ofy=h(x) given, describe each transformation.
3. If the parent function is x2, explain what transformations took place to get the graph below. The vertex is (1,-4)
4
2
– 2
– 4
– 6
– 4 – 2 0 2 4 6 x
y
A B
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Station 2- Writing composition of functions given the description
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1. The graph of a function g is found by starting with the function f ( x )= 1x , then applying the
following transformations: vertical stretch by a factor of 7, translation (shift) 5 units to the right, translation 3 units downwards.
2. . The graph of a function h is found by starting with the function f ( x )=x , then applying the following transformations: translation (shift) 11 units to the left, translation 4 units up.
3. The graph of a function g is found by starting with the function f ( x )=√x, then applying the following transformations: vertical stretch by a factor of 2, translation 21 units to the right.
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Station 3- Graphing composition of functions
Check in!1. Given the graph of y=f (x ), sketch the graph of y=−f ( x+2 ).
2. Given the graph of y=g (x), sketch the graph of y=g (2 x )−1.
3. Given the graph of y=1x , sketch the graph of y= 1
x−1+3.
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4. Given the graph of y=x2, sketch the graph of y= (2x )2−3.
5. Given the graph of y=x2, sketch the graph of y=−( x+5 )2+2.
6. Given the graph of y=√x, sketch the graph of y=√x−3+2.
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Station 4- Bringing it all together/Exam style questions
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1. a. Sketch the graph of f ( x )= 1x2 .
b. For what value of x is f undefined?
c. State the domain and range of f (x).
d. If the graph of f is shifted 4 units right, and 3 units up, the resulting graph is that of the functiong(x ). Find the equation for g(x ).
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2. a. Use your GDC to sketch the graph of the function f ( x )=−√x+2.
b. State the domain and range of f in interval notation.
c. Explain the transformations that occurred to f(x).
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Station 5- Mixed review
1. a. If g ( x )=4 x−5, find g(a−2).
b. If h ( x )= 1+x1−x , find h(1−x).
2. a. Evaluate f (x−3) when f ( x )=2x2−3 x+1.
b. For f ( x )=2x+7 and g ( x )=1−x2, find the composite function defined by ( f ° g )(x ).
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3. Find the inverses of these functions.
a. f ( x )=3 x+172
b. g ( x )=2 x3+3
4. Find the inverse of f ( x )=−15x−1.
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5. Find the inverse functions for
a. f ( x )=3 x+5.
b. f ( x )= 3√x+2 .
6. On the same set of axes, draw the graph of the inverse function.
a. b.
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7. Find the domain and range for each of the functions whose graph is given below.
a. b.
8. For each function, write a single equation to represent the given combination of transformations.
a. f ( x )=√x, stretched vertically by a factor of 2, and translated 3 units left and 2 units down.
b. f ( x )=x2, reflected in the x-axis, translated 5 units right and 1 unit down.
9. Let f ( x )=2x3+3 and g ( x )=3 x−2.
a. Find g(0).
b. Find ( f ∘ g )(0).
c. Find f−1(x).
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8. Let g ¿. The graph of f ( x )=sin (x ) is trandformed to the graph of g. Give a full geometric description of this transformation.
9.
(b) Given: his the graph of ( f ∘ g)(x) after a transformation of 3 units to the right and 1 unit down. Findh.
10.