Limits of Composite Functions

The video tutorial explores the limits of composite functions using the graphs of F(X) and G(X). It covers four main examples: the limit as X approaches -infinity, +infinity, zero, and -1. The tutorial explains how the outputs of F(X) become inputs for G(X) and how this affects the limits. It highlights the behavior of function values as they approach horizontal asymptotes or increase without bound, leading to conclusions about the limits, including cases where limits do not exist.

What is the limit of the composite function g(f(x)) as x approaches -infinity?

• Infinity

• -1

• 0

• 1

As x approaches +infinity, what value does f(x) approach?

• Infinity

• 0

• 1

• -1

What is the limit of g(f(x)) as x approaches +infinity?

• -1

• 0

• 1

• Infinity

As x approaches zero from the positive side, what happens to the values of f(x)?

• They remain constant

• They decrease without bound

• They increase without bound

• They approach zero

What is the limit of g(f(x)) as x approaches zero from the positive side?

• 1

• 0

• Infinity

• -Infinity

As x approaches -1 from the negative side, what value does f(x) approach?

• 1

• Infinity

• 0

• -1

What is the limit of g(f(x)) as x approaches -1 from the negative side?

• 1

• 0

• -Infinity

• Infinity

Which of the following limits does not exist?

• Limit as x approaches -1 from the negative side

• Limit as x approaches zero from the positive side

• Limit as x approaches +infinity

• Limit as x approaches -infinity

What is the behavior of g(x) as x approaches +infinity?

• It decreases without bound

• It increases without bound

• It approaches one

• It approaches zero

What is the final conclusion about the limits of the composite functions discussed?

• All limits are infinite

• Some limits do not exist

• All limits exist

• All limits are zero