4.2 The question seems to be missing some details, but generally speaking, if you're applying a rule to natural numbers smaller than 10, the output numbers would depend on the specific rule used. Since we don't have the specific rule to apply, no detailed answer can be given.
However, as a pointer, the set of natural numbers smaller than 10 are:
1, 2, 3, 4, 5, 6, 7, 8, and 9.
Any rule applied to these numbers would produce a corresponding set of output numbers based on the original numbers.
4.3 If we use the rule "30x + 2" where "x" is the input number, and the input numbers are positive single-digit numbers like 2, 3, and 5, we can calculate the output numbers by applying the rule individually to each input number.
Let's apply the rule "30x + 2" to each number:
- For the input number 2, applying the rule would give us:
30 * 2 + 2 = 60 + 2 = 62
- For the input number 3, applying the rule would give us:
30 * 3 + 2 = 90 + 2 = 92
- For the input number 5, applying the rule would give us:
30 * 5 + 2 = 150 + 2 = 152
Therefore, for the input numbers 2, 3, and 5, by applying the rule "30x + 2," the output numbers we obtain are 62, 92, and 152 respectively. These are all larger than the original numbers and can be considered the transformation of the input numbers by a linear function with a slope of 30 and a y-intercept of 2.
