Question

1. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000

Answer 1

Answer:

See explanation

Step-by-step explanation:

To determine whether each of these functions is $O(x^2)$, we apply these theorems:

1. A polynomial is always O(the term containing the highest power of n)
2. Any O(x) function is always $O(x^2)$.

(a)Given the function: f(x)=100x+1000

The highest power of n is 1.

Therefore f(x) is O(x).

Since any O(x) function is always $O(x^2)$, 100x+1000 is $O(x^2)$.

$(b) f(x)=100x^ 2 + 1000$

The highest power of n is 2.

Therefore the function is $O(x^2)$.