Exponential Functions and Their Properties

The video tutorial covers exponential functions, focusing on graphing y = 3^x and y = (1/4)^x using Desmos. It explains how to plot points on the graph and highlights the behavior of these functions. The tutorial also discusses the domain and range of exponential functions, emphasizing that the domain includes all real numbers while the range consists of positive numbers only.

What is the base of the exponential function discussed in the first example?

• 4

• 3

• 2

• 5

Which point is identified as the y-intercept for the function y = 3^x?

• (0, 1)

• (1, 1)

• (0, 0)

• (1, 0)

What is the behavior of the graph of y = 3^x as x approaches negative infinity?

• It approaches zero

• It approaches infinity

• It remains constant

• It oscillates

What is the base of the exponential function in the second example?

• 1/5

• 1/4

• 1/3

• 1/2

For the function y = (1/4)^x, what is the y-intercept?

• (1, 0)

• (0, 1)

• (1, 1)

• (0, 0)

What happens to the graph of y = (1/4)^x as x becomes more negative?

• It remains constant

• It oscillates

• It approaches infinity

• It approaches zero

What is the domain of the exponential functions discussed?

• All negative numbers

• All positive numbers

• Only integers

• All real numbers

What is the range of the exponential functions discussed?

• All negative numbers

• Only integers

• All positive numbers

• All real numbers

Why do the exponential functions not have negative values in their range?

• They never cross the x-axis

• They are always decreasing

• They never cross the y-axis

• They are always increasing

What is a common characteristic of the domain for both exponential functions discussed?

• It includes only positive numbers

• It includes only negative numbers

• It includes all real numbers

• It includes only integers