Divide a linear equation by a quadratic to determine the domain

The video tutorial explains how to determine the domain of functions, focusing on linear and quadratic functions, which have domains of all real numbers. It highlights the difference when dealing with division, where the denominator cannot be zero, leading to domain restrictions. The concept of movable holes is introduced, explaining that they are discontinuities that affect the domain. Finally, the tutorial demonstrates how to identify domain exclusions using a number line, emphasizing the importance of understanding these concepts in mathematical operations.

What is the domain of a linear function?

• Only negative numbers

• Only integers

• Only positive numbers

• All real numbers

When dividing two functions, what must be considered to determine the domain?

• The product of the functions

• The denominator cannot be zero

• The numerator cannot be zero

• The sum of the functions

What is a removable hole in the context of functions?

• A point where the function is always zero

• A point where the function is undefined but can be simplified

• A point where the function is always positive

• A point where the function is always negative

How do removable holes affect the domain of a function?

• They do not affect the domain

• They create a discontinuity in the domain

• They make the domain only integers

• They make the domain all real numbers

What is the domain of the function f(x) = (x + 3) / (x^2 - 3x)?

• Only negative numbers

• All real numbers except 0 and 3

• All real numbers

• Only positive numbers