Discontinuities and domain of rational functions

The video tutorial covers factoring expressions raised to the third power, focusing on quadratics. It explains how to factor out common terms, identify discontinuities, and find asymptotes. The tutorial also discusses simplifying expressions and determining the domain of functions, emphasizing the importance of understanding the difference of squares and number pairs.

What is the first step in simplifying an expression raised to the third power?

• Add a constant to all terms

• Factor out the common term 'X'

• Multiply all terms by a constant

• Divide all terms by a constant

When solving a quadratic equation, what should the two numbers do?

• Multiply to give a specific product and add to give a specific sum

• Add to give a specific product

• Divide to give a specific quotient

• Multiply to give a specific sum

What is a discontinuity in a rational expression?

• A point where the expression is zero

• A point where the expression is negative

• A point where the expression is undefined

• A point where the expression is infinite

What is an asymptote in the context of rational expressions?

• A line that the graph of the expression approaches but never touches

• A point where the graph of the expression crosses the x-axis

• A point where the graph of the expression crosses the y-axis

• A line that the graph of the expression intersects

How does a hole in a rational expression affect its graph?

• It creates a gap in the graph at a specific point

• It stretches the graph horizontally

• It reflects the graph over the x-axis

• It shifts the graph upwards