Functions and graphs > Transformations

Exercise 1

Start with the basic function $f\left(x\right)=\sqrt{\left(x\right)}$. 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

${y}_{2}=0.5\cdot f\left(x\right)$

b

${y}_{3}=f(x-4)+2$

c

${y}_{4}=2-f\left(x\right)$

d

${y}_{5}=f\left(3x\right)+2$

Exercise 2

Exercise 3

You here see the graph of the function ${y}_{1}=f\left(x\right)$. 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

${y}_{3}=-2\cdot f\left(x\right)$

c

${y}_{4}=f\left(x\right)-2$

d

${y}_{5}=f\left(2x\right)-1$

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?