Use the guidelines for graphing to make a complete graph of
[tex]$f(x)=3 x-5 \sqrt{x}$[/tex]

Start by identifying the domain or interval of interest.
The domain of [tex]$f$[/tex] is ____.
(Type your answer in interval notation.)

Determine the domain of the function f ( x ) = 3 x − 5 x ​ .
Identify that the square root requires x ≥ 0 .
State the domain in interval notation as [ 0 , ∞ ) ​ .

Explanation

Determine the Domain The function given is f ( x ) = 3 x − 5 x ​ . To find the domain, we need to consider any restrictions on the values of x that would make the function undefined. The only potential restriction comes from the square root term, x ​ . The square root of a negative number is not a real number, so we must have x ≥ 0 . Therefore, the domain of f ( x ) is all non-negative real numbers.

State the Domain The domain of f ( x ) is [ 0 , ∞ ) .


Examples
Understanding the domain of a function is crucial in many real-world applications. For example, if f ( x ) represents the production cost of x items, the domain tells us the possible number of items that can be produced. In this case, since the domain is [ 0 , ∞ ) , it means we can produce any non-negative number of items. This is a fundamental concept in economics and business, where understanding the limitations and possibilities of production is essential for making informed decisions.

Answered by GinnyAnswer | 2025-07-05