Answer:
See explanation.
( Conditions of a function )
Explanation:
Declaring Variables:
- The side length of the square = x.
- The area of square = A
- The perimeter of square = P
Solution:
- The area of the square A in terms of side length x is given by:
A(x) = x^2
Where, Area A is dependent on x side length which is independent.
However, the definition of a function does not imply that it should be a straight line , in fact, the function A(x) is not a straight line but a quadratic curve.
According to definition of function i.e the function should be differentiable over all real values of x or its derivative should exist over the entire domain. Hence,
A'(x) = 2*x
- From that we see that A'(x) has real values over the entire domain of x e [ 0 , +inf). Hence, A(x) is a function of x.
- Similarly, The Perimeter of the square P in terms of side length x is given by:
P(x) = 4*x
Where, Perimeter P is dependent on x side length which is independent.
- The function P(x) is a straight line.
- Also, according to definition of function i.e the function should be differentiable over all real values of x or its derivative should exist over the entire domain. Hence,
P'(x) = 4
- From that we see that P'(x) has real values over the entire domain of x e [ 0 , +inf). Hence, P(x) is a function of x.