Graphing Exponential Functions

The video tutorial explains how to graph a basic exponential function by modeling the process of cutting a string. It covers the concept of exponential functions, focusing on exponential decay, and demonstrates how to organize data in a table and graph the results. The tutorial highlights the characteristics of exponential functions, such as the y-intercept and horizontal asymptote, and provides examples of exponential growth and decay. The lesson concludes with a summary of key points and a visual representation of the concepts discussed.

What is the general form of an exponential function?

• y = log(x)

• y = ax^2 + bx + c

• y = b^x

• y = mx + c

How does a negative exponent affect the classification of an exponential function?

• It can change the function from decay to growth.

• It has no effect on the classification.

• It always indicates exponential decay.

• It makes the function linear.

If a string is cut in half repeatedly, what pattern do the lengths follow?

• Random sequence

• Fibonacci sequence

• Geometric sequence

• Arithmetic sequence

What is the y-intercept of the exponential function y = (1/2)^x?

• (1, 0)

• (0, 1)

• (0, 0)

• (1, 1)

What happens to the value of y as x approaches infinity in an exponential decay function?

• y remains constant

• y becomes negative

• y approaches zero

• y approaches infinity

What is a characteristic feature of the graph of an exponential decay function?

• Vertical asymptote

• Horizontal asymptote

• Diagonal asymptote

• No asymptote

In the context of the string cutting example, what does the horizontal asymptote represent?

• The maximum length of the string

• The minimum length of the string

• The original length of the string

• The length of the string after infinite cuts