The video tutorial covers graphing techniques, focusing on rational expressions and asymptotes. It explains how to handle vertical and horizontal asymptotes, emphasizing the importance of understanding algebraic simplification and graphing. The tutorial also discusses limits and how graphs approach asymptotes, providing a comprehensive overview of these mathematical concepts.

Why is it recommended to simplify expressions before graphing?

• Simplification is not necessary before graphing.

• Simplification helps in understanding the function better.

• It makes the graph look more colorful.

• It is a requirement for using a graphing calculator.

How do you determine the presence of a vertical asymptote in a rational function?

• By setting the denominator equal to zero.

• By comparing the degrees of the numerator and denominator.

• By setting the numerator equal to zero.

• By graphing the function directly.

What happens if the square root of a negative number is encountered while finding vertical asymptotes?

• The vertical asymptote does not exist for real numbers.

• The function becomes undefined.

• The vertical asymptote exists for real numbers.

• The graph becomes a straight line.

How is a horizontal asymptote determined in a rational function?

• By setting the numerator equal to zero.

• By finding the roots of the function.

• By setting the denominator equal to zero.

• By comparing the degrees of the numerator and denominator.

What does the horizontal asymptote represent as x approaches infinity?

• The point where the function crosses the x-axis.

• The value the function approaches but never reaches.

• The function's maximum value.

• The function's minimum value.