Functions and graphs > Transformations
12345Transformations

## Solutions to the exercises

Exercise 1
a

Multiply by 1/2 in the $y$ -direction

b

shift $4$ to the right and $2$ up

c

multiply by $-1$ in the $y$ -direction and shift $2$ in the $y$ -direction

d

Multiply by 1/3 in the $x$ -direction and shift $2$ in the $y$ -direction

Exercise 2
• $y={x}^{3}+4$

• $y={\left(x-4\right)}^{3}$

• $y=-0.25{x}^{3}$

• $y={\left(x-2\right)}^{3}-$ 4`

Exercise 3
a

b

c

d

Exercise 4
a

shift $y=-{x}^{2}$ in the $x$ -direction by $10$ and in the $y$ -direction by $4$
Use $0\le x\le 25$. Since there is a multiplication with factor $0.02$, it is sufficient to use $0\le y\le 5$.

b

$24.14$ m

c

$20$ m.