Behavior of Exponential Functions

The video tutorial explains how functions with negative exponents behave. It highlights that a negative exponent indicates a reciprocal, affecting whether a function is increasing or decreasing. For example, a function with a base less than one and a negative exponent is increasing, while a base greater than one results in a decreasing function. The reciprocal property is key to understanding these behaviors.

What does a negative exponent indicate in a function?

• It indicates a derivative.

• It indicates a logarithm.

• It indicates a square root.

• It indicates a reciprocal.

What is the effect of a negative exponent on the base of a function?

• It squares the base.

• It takes the reciprocal of the base.

• It doubles the base.

• It halves the base.

What is the equivalent function of y = 1/2^(-x)?

• y = 2^x

• y = 1/2^x

• y = 2^(-x)

• y = 1/4^x

What is the reciprocal of 1/2?

• 2

• 1

• 4

• 1/4

Which function is equivalent to y = 1/2^(-x)?

• y = 1/4^x

• y = 2^x

• y = 4^x

• y = 1/2^x

How does the function y = 1/2^(-x) behave as x increases?

• It decreases.

• It remains constant.

• It increases.

• It oscillates.

If y = 1/2^(-x) is increasing, what can be said about y = 2^x?

• It is decreasing.

• It is constant.

• It is increasing.

• It is oscillating.

What is the equivalent function of y = 3/2^(-x)?

• y = 2/3^x

• y = 3/2^x

• y = 2^x

• y = 1/3^x

What happens to a function when the base is greater than 1 and the exponent is negative?

• The function becomes constant.

• The function decreases.

• The function increases.

• The function oscillates.

In the function y = 3/2^(-x), what is the base of the equivalent function?

• 3/2

• 2/3

• 1/3

• 1/2