Exponential Functions and Their Properties

The video tutorial explains how to graph exponential functions of the form y = B^x, where B is a constant like 2, 3, or 10. It demonstrates the process of plotting these functions by calculating values for different x inputs, including negative exponents. The tutorial highlights the common features of these graphs, such as their asymptotic behavior towards y = 0 and the shared point at (0, 1). The video also compares the graphs of y = 2^x, y = 3^x, and y = 10^x, noting their similarities and differences in steepness and height.

What is the general form of an exponential function?

• y = log(x)

• y = x^2

• y = B^x

• y = mx + b

What is the value of y when x = 0 in the function y = 2^x?

• 2

• Undefined

• 0

• 1

How does the graph of y = 2^x behave as x becomes more negative?

• It approaches zero but never touches it.

• It becomes a straight line.

• It increases indefinitely.

• It oscillates.

What is the y-value when x = -1 for the function y = 2^x?

• 1/2

• 2

• 0

• 1

What is the y-value when x = 1 for the function y = 3^x?

• 3

• 9

• 2

• 1

Which point is common to both y = 2^x and y = 3^x?

• (0, 0)

• (1, 1)

• (0, 1)

• (1, 0)

What happens to the graph of y = 3^x as x becomes more negative?

• It oscillates.

• It becomes a straight line.

• It increases indefinitely.

• It approaches zero but never touches it.

What is the value of y when x = 2 in the function y = 10^x?

• 10

• 100

• 1000

• 20

How does the graph of y = 10^x compare to y = 2^x and y = 3^x?

• It is steeper.

• It is the same.

• It is flatter.

• It is a straight line.

What is a common feature of all exponential graphs discussed?

• They all decrease as x increases.

• They all have a maximum point.

• They all have an asymptote at y = 0.

• They all pass through (0, 0).