Vertical Asymptotes of h(t) = (t^2 - 2t)/(t^4 - 16) | Summary and Q&A

TL;DR

The video explains how to find vertical asymptotes of rational functions, emphasizing simplification and setting the denominator equal to zero.

Key Insights

• 🚦 Simplifying the rational function is the first step in finding vertical asymptotes.
• 😫 Setting the denominator equal to zero helps identify potential vertical asymptotes.
• 🍉 Quadratic terms with no real solutions do not contribute to vertical asymptotes.

Transcript

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Questions & Answers

Q: Why is simplifying the rational function the first step in finding vertical asymptotes?

Simplification allows us to identify any common factors that can be canceled out, making the function easier to work with and reducing the likelihood of unnecessary complexity in determining the vertical asymptotes.

Q: How do you determine potential vertical asymptotes?

To find potential vertical asymptotes, set the denominator equal to zero. Any value of the variable that makes the denominator zero could be a vertical asymptote.

Q: What does it mean when the quadratic term in the denominator has no real solutions?

If the quadratic term in the denominator has no real solutions, it means that there are no vertical asymptotes in that particular section of the graph. This is because the quadratic term is always positive, preventing the function from approaching infinity or negative infinity.

Q: Can a rational function have multiple vertical asymptotes?

Yes, a rational function can have multiple vertical asymptotes. The number of vertical asymptotes depends on the factors in the denominator after simplification. Each distinct factor that causes the denominator to be zero corresponds to a vertical asymptote.

Summary & Key Takeaways

• To find vertical asymptotes of rational functions, simplify the function if possible.

• Set the denominator equal to zero to determine potential vertical asymptotes.

• In the given example, the vertical asymptote is t = -2.