Exploring Exponential Functions and Graphing Techniques

This video introduces exponential functions, contrasting them with linear functions. It explains the concept of exponential growth and decay, and demonstrates how to graph these functions using Desmos. The video includes examples of exponential growth and decay, showing how to input equations and interpret graphs. It also covers how to access and copy tables of values from Desmos, rounding values to the nearest hundredth. The lesson concludes with a brief overview of the key concepts, preparing students for more in-depth exploration in future lessons.

What type of functions did we study before exponential functions?

• Linear functions

• Trigonometric functions

• Cubic functions

• Quadratic functions

What is the general form of an exponential function?

• y = a / b^x

• y = a * b^x

• y = ax^b

• y = a + bx

In the equation y = a * b^x, what condition must 'b' satisfy for exponential growth?

• b = 1

• b < 0

• b < 1

• b > 1

How do you access the table of values in Desmos?

• Click on the 'graph' button

• Click on the 'settings gear' then 'table'

• Type 'table' in the search bar

• Click on the 'data' tab

What does the graph of y = 2^x represent?

• Exponential growth

• Constant function

• Linear growth

• Exponential decay

What value does y = 2^x have when x = 0?

• 0.5

• 2

• 1

• 0

What does the graph of y = (1/2)^x represent?

• Oscillation

• Linear decay

• Exponential growth

• Exponential decay

What is the value of y = (1/2)^x when x = 2?

• 1

• 0.25

• 0.5

• 2

What is the behavior of the graph of y = (2/3)^x?

• Exponential growth

• Exponential decay

• Linear growth

• No change

What does rounding to the nearest hundredth mean?

• Rounding to the nearest 0.01

• Rounding to the nearest 0.1

• Rounding to the nearest 1

• Rounding to the nearest 10