Exponential Functions and Their Properties

This video tutorial covers exponential functions, including their definition, properties, and how to graph them. It explains the difference between exponential growth and decay, and provides examples of each. The video also discusses the characteristics of exponential graphs, such as y-intercepts and asymptotes, and explores real-life applications like population growth and radioactive decay. Additionally, it highlights the symmetry in exponential functions and encourages viewers to practice graphing without a calculator.

What is the condition for a function to be classified as exponential growth?

• The base is greater than 1

• The base is between 0 and 1

• The base is equal to 1

• The base is less than 0

Which of the following is true for an exponential decay function?

• It is a positive decreasing function

• It is a positive increasing function

• It is a negative increasing function

• It is a negative decreasing function

What is the y-intercept of the function f(x) = 2^x?

• (0, 0)

• (0, 1)

• (1, 1)

• (1, 0)

What happens to the y-values of the function f(x) = 2^x as x approaches negative infinity?

• They approach 0

• They approach 1

• They approach 2

• They approach infinity

In the graph of f(x) = (1/2)^x, what is the behavior of the function?

• It decreases from left to right

• It increases from left to right

• It oscillates

• It remains constant

What is the horizontal asymptote of the function f(x) = (1/2)^x?

• y = x

• y = -1

• y = 0

• y = 1

What is the result of reflecting the graph of f(x) = 2^x across the y-axis?

• f(x) = -2^-x

• f(x) = -2^x

• f(x) = 2^-x

• f(x) = 2^x

Which of the following is an example of exponential growth?

• Population growth

• Radioactive decay

• Cooling of a hot object

• Medication dosage

Which real-life scenario is an example of exponential decay?

• Bacteria growth

• Internet user growth

• Population growth

• Radioactive decay

What is the significance of the website INTMATH.com mentioned in the video?

• It predicts the exact population in 2050

• It offers a dynamic view of world population growth

• It shows the rate of population decrease

• It provides a static view of world population