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

Station 2- Writing composition of functions given the description

Check in!

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.

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.

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.

Station 4- Bringing it all together/Exam style questions

Check in !

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 ).

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).

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 ).

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.

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.

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).

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.