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Have you ever seen fractions in mathematics? Well, rational functions are similar to fractions, but more interesting because they involve variables!
A rational function is a function in the form of a fraction, where both the numerator and denominator are polynomial functions. Simply put, a rational function can be written as:
Where:
Let's look at a real example to better understand rational functions.
Chicken Coop Problem:
Mr. Budi wants to build a rectangular chicken coop with an area of . He wants to know the relationship between the length and width of the coop.
If the length of the coop is , then:
The function is an example of a rational function!
The simplest form of a rational function:
Where is a constant. Example:
Both numerator and denominator are linear functions:
Example:
Involves quadratic functions in the numerator or denominator:
The domain of a rational function is all values of that make the function defined. Remember, the denominator cannot be zero!
How to find the domain:
Example: Determine the domain of
Solution:
Rational functions can be simplified by finding common factors in the numerator and denominator.
Simplify:
Solution:
Simplify:
Solution:
Note: (from the original domain)
Just like regular fractions, we need to find a common denominator first!
Example:
Solution:
Multiply numerator with numerator, denominator with denominator:
Example:
Solution:
Remember, dividing means multiplying by the reciprocal:
Determine the domain of
Simplify
Calculate
A car travels . If the average speed is , write the travel time function in terms of .
Answer :
Domain:
Answer :
With the condition
Answer :
Answer :
