Understanding Vertical Asymptotes

This video tutorial explains how to find vertical asymptotes of functions. It covers various methods, including setting the denominator to zero, using the difference of squares, and factoring trinomials. The video also addresses cases with imaginary solutions and provides a complex example using factoring by grouping. Each method is demonstrated with examples to enhance understanding.

What is the vertical asymptote of the function 1/(x-3)?

• x = 3

• x = 1

• x = 0

• x = -3

How do you find the vertical asymptotes of 4/(x^2 - 16)?

• Set x^2 + 4 = 0

• Set x^2 - 4 = 0

• Set x^2 + 16 = 0

• Set x^2 - 16 = 0

What are the vertical asymptotes of 4/(x^2 - 16)?

• x = 8 and x = -8

• x = 2 and x = -2

• x = 0 and x = 4

• x = 4 and x = -4

In the function (3x-6)/(x^2-7x+10), what is the vertical asymptote after canceling common factors?

• x = 2

• x = 5

• x = -5

• x = 0

Why is x = 2 not a vertical asymptote in the function (3x-6)/(x^2-7x+10)?

• It is an intercept

• It is undefined

• It is a hole

• It is a zero

What happens when the denominator of a function equals a negative number under a square root?

• It results in a vertical asymptote

• It results in a hole

• It results in an imaginary solution

• It results in a zero

Why can't imaginary solutions create vertical asymptotes?

• They are intercepts

• They are not real numbers

• They are undefined

• They are zeros

In the function 10x^2 - 5x - 15, what is the first step in factoring?

• Remove the GCF

• Set the equation to zero

• Divide by x

• Multiply by a constant

What is the vertical asymptote of the function 10x^2 - 5x - 15 divided by 6x^2 - 17x + 12?

• x = 3/4

• x = 4/3

• x = 3/2

• x = 2/3

What is the result of canceling common factors in the function 10x^2 - 5x - 15 divided by 6x^2 - 17x + 12?

• x = 3/4

• x = 2/3

• x = 3/2

• x = 4/3