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Exercises

Exercise 1

Start with the basic function f ( x ) = ( x ) . You can construct the graphs of the following functions by transforming this basic function. For each one, indicate what sort of transformation is required.

a

y 2 = 0 . 5 f ( x )

b

y 3 = f ( x - 4 ) + 2

c

y 4 = 2 - f ( x )

d

y 5 = f ( 3 x ) + 2

Exercise 2

Here you see five windows of a graphing calculator with the standard settings. The graph on the right is that of the function . The other four graphs have been derived by transforming this function. For each graph, write down the correct function rule.

a
b
c
d
Exercise 3

You here see the graph of the function y 1 = f ( x ) . Draw the same graph on a separate sheet of graphing paper. On the same sheet, draw the graphs of the following functions. For each one, describe which transformation you are using.

a

y 2 = f ( x - 2 )

b

y 3 = - 2 f ( x )

c

y 4 = f ( x ) - 2

d

y 5 = f ( 2 x ) - 1

Exercise 4

A ball thrown by a shotputter describes the following trajectory in an x,y-coordinate system: y = - 0 . 02 ( x - 10 ) 2 + 4 .
At the point of release, we have and . y and x are both given in metres

a

Describe, using transformations, how you determine the plotting window for your graphing calculator to displaly the entire trajectory of the ball.

b

Calculate how far this shotputter has thrown the ball.

c

What distance has the ball covered before it returns to the height it had at the point of release?

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