Exponential Decay Functions Concepts

This screencast is the second in a series on exponential function graphs, focusing on exponential decay. It explains the general properties of exponential decay functions, how to graph them, and analyzes specific examples, including a complex function with transformations. The video covers the domain, range, and behavior of these functions, emphasizing the differences between growth and decay.

What is the focus of this screencast?

• Quadratic functions

• Linear functions

• Exponential decay functions

• Exponential growth functions

In an exponential decay function, what is the range of the base?

• Equal to 1

• Greater than 1

• Less than 0

• Between 0 and 1

What happens to the value of an exponential decay function as x increases?

• It increases

• It oscillates

• It decreases

• It remains constant

What is the y-intercept of the function y = (1/5)^x?

• (0, 0)

• (1, 1)

• (0, 1)

• (1, 0)

How does the graph of y = 5^x compare to y = (1/5)^x?

• Both are increasing

• 5^x is increasing, (1/5)^x is decreasing

• Both are decreasing

• 5^x is decreasing, (1/5)^x is increasing

What transformation occurs when a negative sign is placed in front of an exponential function?

• Vertical stretch

• Reflection about the y-axis

• Horizontal shift

• Reflection about the x-axis

What is the domain of an exponential decay function?

• Numbers between 0 and 1

• All negative numbers

• All positive numbers

• All real numbers

What is the range of the function y = -4 * (1/2)^(x-1) + 2?

• Y values between 0 and 2

• Y values less than 2

• Y values greater than 2

• All real numbers

What is the limit of the function y = -4 * (1/2)^(x-1) + 2 as x approaches infinity?

• 0

• 1

• 2

• Negative infinity