Limits & Asymptotes: A Precalculus Challenge for 11th Graders

A car's speed is modeled by the function v(t) = 60/(1 + e^(-0.1t)), where t is time in hours. What is the limit of the car's speed as time approaches infinity?

• 75

• 60

• 45

• 30

The function f(x) = (2x^2 - 8)/(x^2 - 4) has a vertical asymptote. Identify the value of x where this asymptote occurs.

• x = 0

• x = 3

• x = 2, x = -2

• x = 1

Tags

CCSS.HSF-IF.C.7D

A company's profit P(x) is given by P(x) = (100x)/(x^2 + 10). Determine the limit of the profit as the number of units sold approaches infinity.

• 10

• 0

• Infinity

• 100

Tags

CCSS.HSF-IF.C.8B

The function g(x) = (3x + 1)/(x - 2) has a horizontal asymptote. What is the value of this asymptote?

• 1

• 4

• 2

• 3

Tags

CCSS.HSF-IF.C.7D

A population of bacteria is modeled by the function N(t) = 100/(1 + 0.5e^(-0.2t)). What is the limit of the population as time t approaches infinity?

• 75

• 100

• 200

• 50

The function h(x) = (x^2 - 1)/(x^2 + 1) has a horizontal asymptote. Calculate this asymptote as x approaches infinity.

• y = 1

• y = 0

• y = 2

• y = -1

Tags

CCSS.HSF-IF.C.7D

A rocket's height is modeled by the function h(t) = 100t/(t + 5). What is the limit of the height as time t approaches infinity?

• 100

• 200

• 50

• t

The function j(x) = (x^2 - 4)/(x - 2) has a removable discontinuity. Identify the x-value where this occurs and explain how it relates to limits.

• 0

• 4

• 2

• -2

Tags

CCSS.HSF-IF.C.7D

A tank is filled with water according to the function W(t) = 50/(1 + e^(-0.1t)). What is the limit of the water volume as time t approaches infinity?

• 100

• 25

• 75

• 50

Tags

CCSS.HSF-IF.C.8B

The function k(x) = (5x)/(x^2 - 1) has vertical asymptotes. Identify the x-values where these asymptotes occur and explain their significance.

• x = 0

• x = -2

• x = 2

• x = 1 and x = -1

Tags

CCSS.HSF-IF.C.7D