Exponential Decay Function Concepts

The video tutorial explains the parent exponential function f(x) = a^x, where a is positive and not equal to 1. It covers the domain and range of exponential functions, highlighting that the domain is all real numbers and the range is positive values excluding zero. The tutorial distinguishes between exponential growth and decay, explaining that growth occurs when a > 1, and decay when a is a fraction between 0 and 1. Key characteristics such as intercepts, continuity, and the behavior of the function as x increases are discussed for both growth and decay scenarios.

What is the domain of the parent exponential function f(x) = a^x?

• All negative numbers

• All positive numbers

• All real numbers

• Only integers

Which of the following is true about the range of the parent exponential function?

• It is limited to positive integers

• It includes negative numbers

• It starts from zero but does not include it

• It includes zero

What is the y-intercept of the parent exponential function?

• (1, 0)

• (0, 0)

• (1, 1)

• (0, 1)

Why does the parent exponential function not have an x-intercept?

• Because it has a horizontal asymptote at y = 0

• Because it is a linear function

• Because it is a decreasing function

• Because it is not defined for x = 0

What happens to the function f(x) = a^x as x increases?

• It decreases

• It remains constant

• It increases

• It oscillates

What is the base condition for the function f(x) = a^(-x) to indicate exponential decay?

• a < 1

• a = 1

• a > 1

• a = 0

How can the base of the function f(x) = a^(-x) be transformed to indicate decay?

• By making it a fraction between 0 and 1

• By making it a negative number

• By making it greater than 1

• By making it equal to 1

What is the horizontal asymptote of the exponential decay function?

• y = 0

• x = 0

• y = 1

• x = 1

What is the behavior of the exponential decay function as x increases?

• It remains constant

• It increases

• It decreases

• It oscillates

What does it mean for the exponential decay function to be continuous?

• It is only defined for positive values

• It can be drawn without lifting the pen

• It is only defined for integer values

• It has breaks in the graph