Exploring Limits and Asymptotes

What happens when the power on top is less than the power on bottom?

• No asymptote

• Vertical asymptote at x=0

• Horizontal asymptote at y=1

• Horizontal asymptote at y=0

How do you find a vertical asymptote for a rational function?

• Set the numerator equal to zero

• Find the zeros of the denominator

• Multiply the numerator and denominator

• Add the highest powers of numerator and denominator

What indicates a hole in the graph of a rational function?

• A zero in the denominator

• Common factors in numerator and denominator

• Different powers in numerator and denominator

• A zero in the numerator

For the function f(x) = 2/(x-3), what is the domain?

• x > 3

• All real numbers

• All x except x=0

• All x except x=3

What is the y-intercept of the function f(x) = 2/(x-3)?

• y = 3

• y = 0

• y = 2/3

• y = -2/3

For the function f(x) = (2x+3)/(x+1), what is the horizontal asymptote?

• y = 0

• y = 2

• No horizontal asymptote

• y = 3

What is the x-intercept of the function f(x) = (2x+3)/(x+1)?

• No x-intercept

• x = 1

• x = -3/2

• x = 3/2

In the function f(x) = (x-3)/(x^2-2x-3), what simplification leads to a hole in the graph?

• Cancelling x+1

• Factoring x^2-2x-3

• Multiplying numerator and denominator

• Cancelling x-3

What is the y-value of the hole in the graph of f(x) = (x-3)/(x^2-2x-3)?

• -1

• 1/4

• 1/2

• 3

For the simplified function f(x) = 1/(x+1), what is the vertical asymptote?

• x = 1

• x = 0

• No vertical asymptote

• x = -1