Exponential Functions Behavior and Properties

The video tutorial explains how to determine if an exponential function is increasing or decreasing based on its base value. If the base is between 0 and 1, the function decreases as it is multiplied by itself. Conversely, if the base is greater than 1, the function increases, growing larger with each multiplication. Examples of both decreasing and increasing exponential functions are provided to illustrate these concepts.

What determines whether an exponential function is increasing or decreasing?

• The base value

• The exponent value

• The initial value

• The domain of the function

When is an exponential function considered decreasing?

• When the base is equal to 1

• When the base is greater than 1

• When the base is less than 0

• When the base is between 0 and 1

Why do exponential functions with a base between 0 and 1 decrease?

• Because they multiply to become smaller

• Because they multiply to become larger

• Because they remain constant

• Because they approach infinity

What is the result of multiplying a fraction by itself multiple times?

• It becomes larger

• It oscillates

• It becomes smaller

• It remains the same

Which of the following is an example of a decreasing exponential function?

• y = 10^x

• y = 1^x

• y = 0.5^x

• y = 2^x

What happens to the value of y = (1/3)^x as x increases?

• It increases

• It decreases

• It oscillates

• It remains constant

Which of the following functions will decrease as x increases?

• y = 10^x

• y = 2^x

• y = 1.5^x

• y = 0.8^x

What is the behavior of y = 0.23^x as x increases?

• It increases

• It oscillates

• It decreases

• It remains constant

When is an exponential function considered increasing?

• When the base is between 0 and 1

• When the base is greater than 1

• When the base is less than 0

• When the base is equal to 1

Why do exponential functions with a base greater than 1 increase?

• Because they remain constant

• Because they multiply to become smaller

• Because they multiply to become larger

• Because they approach zero