Question

Recall that the perimeter of a square is 4 times as large as the length of one of the sides of the square. Let x represent the length of one side of a square (in inches), and let y represent the perimeter of that square (in inches).
y is a function of x, so we can define a function f to represent this relationship (e.g.(x)=y).
Write a function formula for the function f.

What is the (practical) domain of the function f? Enter your answer as an inequality.

What is the (practical) range of the function f? Enter your answer as an inequality.

Assume the square can have a side length of 0 inches.

Answer 1

• The required function formula for the function "f" is $f(x) = 4x$

• Since the side length of the square cannot be positive, hence the domain will be values from 0 and above i.e. Domain = 0≤x≤∞

• The range of the function will be 4≤f(x)≤∞

The perimeter of a square is expressed according to the formula:

P = 4L

P is the perimeter of the square

L is the side length of the square

Given the following

Perimeter is y

Length is x

The function that represents the statement is expressed as $y=4x$

The required function formula for the function "f" is $f(x) = 4x$

The domain of the function is the value of the input value for which the function exists

• Since the side length of the square cannot be positive, hence the domain will be values from 0 and above i.e. Domain = 0≤x≤∞

The range of the function is the value of the output value f(x) for which the function exists, hence;

• The range of the function will be 4≤f(x)≤∞

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