❖ Finding the Domain of a Function Algebraically (No graph!) ❖

Finding the Domain of a Function Algebraically - Step-by-Step Examples!

Description: In this video, I walk through finding the domain of a function algebraically—without using any graphs! We'll cover two key examples.

In the first example, we analyze a rational function where we need to exclude values of 𝑥 that result in a zero denominator. This helps us determine the valid domain of the function.

In the second example, we solve a linear inequality to ensure that we don’t end up with negative numbers under a square root.

Each of these examples is fundamental and widely applicable, appearing throughout algebra, precalculus, calculus, and more. Whether you're learning about domains for the first time or need a refresher, these examples will help you master finding domains algebraically.

What You Will Learn:

How to find the domain of rational functions by excluding zero denominators
How to solve linear inequalities to ensure non-negative square root values
The foundational skills for determining the domain of a function without graphing

Support my work on Patreon for more math content:

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[patrickjmt]

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[falgsc]

If it is a quadratic or two quadratic functions in ratio, one can equate it to y, transpose all the terms to one side, find the Discriminant of the resulting quadratic, one finds a quadratic with y. Equate this quadratic to an inequality as greater than or equal to 0, solve the inequality, and that is the range of the function..

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[jademwayson]

how do you find the range of a function algebraically?

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