Start with the basic function . You can construct the graphs of the following functions by transforming this basic function. For each one, indicate what sort of transformation is required.
Here you see five windows of a graphing calculator with the standard settings. The graph on the right is that of the function `y_1=x^3` . The other four graphs have been derived by transforming this function. For each graph, write down the correct function rule.
You here see the graph of the function . 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 ball thrown by a shotputter describes the following trajectory in an x,y-coordinate system: .
At the point of release, we have
`y=2`
and
`x=0`
. and are both given in metres
Describe, using transformations, how you determine the plotting window for your graphing calculator to displaly the entire trajectory of the ball.
Calculate how far this shotputter has thrown the ball.
What distance has the ball covered before it returns to the height it had at the point of release?