Exponential Functions and Their Properties

The video introduces exponential functions, highlighting their differences from linear functions. It covers evaluating exponential functions, calculating average rates of change, and graphing them using a calculator. The behavior of exponential functions is explained based on their base values, distinguishing between growth and decay. The video also demonstrates how to identify exponential functions from tables and concludes with real-world applications.

What distinguishes exponential functions from linear functions?

• Exponential functions have constant rates of change.

• Exponential functions graph as straight lines.

• Exponential functions graph as curved lines.

• Exponential functions are a type of linear function.

What is the value of f(2) for the function f(x) = 8 * 2^x?

• 4

• 16

• 32

• 8

Which point lies on the graph of f(x) = 8 * 2^x when x = 0?

• (0, 32)

• (0, 8)

• (0, 1)

• (0, 16)

How do you calculate the average rate of change for a function over an interval?

• Subtract the x-values and divide by the y-values.

• Subtract the y-values and divide by the x-values.

• Add the x-values and y-values.

• Multiply the x-values and y-values.

What does a non-constant average rate of change indicate about a function?

• The function is constant.

• The function is quadratic.

• The function is linear.

• The function is exponential.

What is the y-intercept of the function f(x) = 8 * 2^x?

• 0

• 2

• 16

• 8

What does the base of an exponential function determine?

• The y-intercept of the function.

• The slope of the function.

• Whether the function increases or decreases.

• The x-intercept of the function.

For the function g(x) = 54 * (1/3)^x, what is the y-intercept?

• 54

• 18

• 0

• 1/3

How do you determine if an exponential function is increasing?

• The base is less than 1.

• The base is greater than 1.

• The base is equal to 1.

• The base is negative.

What is the equation of an exponential function with a y-intercept of 10 and a base of 3?

• y = 3 + 10x

• y = 10 + 3x

• y = 3 * 10^x

• y = 10 * 3^x