Multiple Choice

For #1 to #6, choose the best answer.

1.The graph y f (x) contains the point (3, 4). After a transformation, the point (3, 4) is transformed to (5, 5). Which of the following is a possible equation of the transformed function?

Ay 1 f (x 2)

By 1 f (x 2)

Cy 1 f (x 2)

Dy 1 f (x 2)

2.The graph of y x is transformed by a vertical stretch by a factor of 3 about the x-axis, and then a horizontal translation of

3 units left and a vertical translation up

1 unit. Which of the following points is on the transformed function?

A(0, 0)

B(1, 3)

C(3, 1)

D(3, 1)

3.The graph of is vertically stretched by a factor of 2 about the x-axis, then reflected about the y-axis, and then horizontally translated left 3. What is the equation of the transformed function?

A

B

C

D

4.Which of the following transformations would produce a graph with the same x-intercepts as y f (x)?

Ay f (x)

By f (x)

Cy f (x 1)

Dy f (x) 1

5.Given the graph of y f (x), what is the invariant point under the transformation y f (2x)?

A(1, 0)B(0, )

C(1, 1)D(3, 1)

6.What will the transformation of the graph of y f (x) be if y is replaced with y in the equation y f (x)?

AIt will be reflected in the x-axis.

BIt will be reflected in the y-axis.

CIt will be reflected in the line y x.

DIt will be reflected in the line y 1.

Short Answer

7.If the range of function y f (x) is {y y 4}, state the range of the new function g(x) f (x 2) 3.

8.As a result of the transformation of the graph of y f (x) into the graph of y 3f (x 2) 5, the point (2, 5) becomes point (x, y). Determine the value of (x, y).

9.The graph of f (x) is stretched horizontally by a factor of about the y-axis and then stretched vertically by a factor of about

the x-axis. Determine the equation of the transformed function.

10.A function f (x) x2 x 2 is multiplied by a constant value k to create a new function g(x) k f (x). If the graph of y g(x) passes through the point (3, 14), state the value of k.

Extended Response

11.Sketch the graph of the inverse relation.

b)

b)

a)

a) If the point (1, 1) on y f (x) maps onto the point (1, 2) on y g (x), describe the transformation and state the equation of g (x).

b)If the point (4, 2) on y f (x) maps onto the point (1, 2) on y g (x), describe the transformation and state the equation of g (x).

b) If the point (1, 1) on y f (x) maps onto the point (1, 2) on y g (x), describe the transformation and state the equation of g (x).

b)If the point (4, 2) on y f (x) maps onto the point (1, 2) on y g (x), describe the transformation and state the equation of g (x).

12.The graphs of y f (x) and y g(x) are shown.

13.Consider the graph of the function y f (x).

a) Describe the transformation of

y f (x) to y 3f (2 (x 1)) 4.

b)Sketch the graph.

b) Describe the transformation of

y f (x) to y 3f (2 (x 1)) 4.

b)Sketch the graph.

14.A function is defined by

f (x) (x 2)(x 3).

a)If g(x) kf (x), describe how k affects the y-intercept of the graph of the function y g(x) compared to y f (x).

b)If h(x) f (mx), describe how m affects the x-intercepts of the graph of the function y h(x) compared to y f (x).

15.Complete the following for the quadratic function f (x) x2 2x 1.

a)Write the equation of f(x)...