Consider the input numbers: 3, 5, 7, 9, 11. Rule: 2x. Represent your answers using a flow diagram. Write down the rule for the following input and output values. Input values: 2, 4, 6, 8, 10 Output va

• For $x=3$: $2(3) = 6$
• For $x=5$: $2(5) = 10$
• For $x=7$: $2(7) = 14$
• For $x=9$: $2(9) = 18$
• For $x=11$: $2(11) = 22$

The output numbers are $\boxed{6, 10, 14, 18, 22}$.

3.1.2
Represent your answers using a flow diagram.

3.2
Write down the rule for the following input and output values.

Input values: 2, 4, 6, 8, 10
Output values: 3, 15, 35, 63, 99

• For input 2, output 3: $2^2 - 1 = 4 - 1 = 3$
• For input 4, output 15: $4^2 - 1 = 16 - 1 = 15$
• For input 6, output 35: $6^2 - 1 = 36 - 1 = 35$
• For input 8, output 63: $8^2 - 1 = 64 - 1 = 63$
• For input 10, output 99: $10^2 - 1 = 100 - 1 = 99$

The rule is $\boxed{x^2 - 1}$.

3.3
What kind of outputs will be obtained by applying the rule $-2x$ to all negative integers?

• If $x = -1$, output is $-2(-1) = 2$.
• If $x = -2$, output is $-2(-2) = 4$.
• If $x = -3$, output is $-2(-3) = 6$.

The outputs will be $\boxed{positive even integers}$.

3.4
What kind of outputs will be obtained by applying the rule $\frac{x}{5}$ to natural numbers smaller than 5?

Natural numbers are positive integers (1, 2, 3, ...). So, natural numbers smaller than 5 are 1, 2, 3, 4.

• For $x=1$: $\frac{1}{5}$
• For $x=2$: $\frac{2}{5}$
• For $x=3$: $\frac{3}{5}$
• For $x=4$: $\frac{4}{5}$

The outputs will be $\boxed{positive proper fractions}$.