Functions and graphs

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

$y = x^{3} + 4$
$y = {(x - 4)}^{3}$
$y = - 0.25 x^{3}$
$y = {(x - 2)}^{3} -$ 4`

Exercise 3

a

Let your teacher check this.

b

Let your teacher check this.

c

Let your teacher check this.

d

Let your teacher check this.

Exercise 4

a

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

b

$24.14$ m

c

$20$ m.

Solutions to the exercises