Limits Involving Infinity and Asymptotes

Question 1

What does the notation `lim (x→∞) f(x) = L` signify for a function f(x)?

Accepted Answer

The function f(x) approaches L as x becomes infinitely large.

Answer

The function f(x) approaches L as x approaches zero.

Answer

The function f(x) is equal to L at infinity.

Answer

The function f(x) is undefined at infinity.

Question 2

A horizontal asymptote of a rational function `f(x) = P(x)/Q(x)` exists if the degree of the numerator P(x) is:

Accepted Answer

Less than or equal to the degree of the denominator Q(x).

Answer

Greater than the degree of the denominator Q(x).

Answer

Strictly less than the degree of the denominator Q(x).

Answer

Exactly one greater than the degree of the denominator Q(x).

Question 3

What is the horizontal asymptote of the function `f(x) = (3x + 5) / (2x^2 + 1)`?

Accepted Answer

y = 0

Answer

y = 3/2

Answer

x = 0

Answer

No horizontal asymptote

Question 4

Determine the horizontal asymptote for the function `g(x) = (4x^2 - 7) / (2x^2 + 3x)`.

Accepted Answer

y = 2

Answer

y = 0

Answer

y = 4/3

Answer

x = -3/2

Question 5

Vertical asymptotes of a rational function `f(x) = P(x)/Q(x)` typically occur at values of x where:

Accepted Answer

`Q(x) = 0` and `P(x) ≠ 0`

Answer

`P(x) = 0` and `Q(x) ≠ 0`

Answer

Both `P(x) = 0` and `Q(x) = 0`

Answer

`lim (x→∞) f(x)` is a finite value.

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