Understanding Limits and Asymptotes

What is the limit of the function y = 1/x as x approaches infinity?

• 0

• 1

• -Infinity

• Infinity

When simplifying the limit of a rational function, why do we divide by the highest power in the denominator?

• To make the numerator zero

• To simplify the expression

• To eliminate the denominator

• To find the horizontal asymptote

What happens to the limit of a rational function if the degree of the numerator is less than the degree of the denominator?

• The limit is 1

• The limit is 0

• The limit is infinity

• The limit does not exist

How does the degree of a polynomial affect its end behavior?

• It determines the horizontal asymptote

• It affects the vertical asymptote

• It dictates the behavior at infinity

• It has no effect

For a polynomial with an even degree and a positive leading coefficient, what is the end behavior as x approaches negative infinity?

• The function approaches zero

• The function oscillates

• The function approaches positive infinity

• The function approaches negative infinity

What is the end behavior of an exponential growth function as x approaches infinity?

• The function remains constant

• The function approaches zero

• The function approaches negative infinity

• The function approaches positive infinity

In an exponential decay function, what happens as x approaches negative infinity?

• The function approaches zero

• The function approaches positive infinity

• The function approaches negative infinity

• The function remains constant

What is the limit of e^x as x approaches negative infinity?

• Negative infinity

• One

• Zero

• Infinity

What is the behavior of the natural logarithm function as x approaches infinity?

• It approaches zero

• It approaches negative infinity

• It remains constant

• It increases without bound

Why can't we evaluate the limit of ln(x) as x approaches negative infinity?

• The limit is zero

• Logarithms are not defined for negative numbers

• The function oscillates

• The limit is infinity