Exploring Exponential Functions and Their Graphs

This video tutorial by Mr. Banker covers exponential functions, their properties, and how to identify them. It explains how to compute values of exponential functions and derive them from tables. The video also discusses exponential growth and decay models, and explores transformations of exponential functions and their graphical effects.

What is the base of an exponential function if it cannot be which of the following values?

• A positive integer

• A negative integer

• 1

• 0

If f(x) = 3^x, what is the initial value?

• Undefined

• 1

• 0

• 3

In the function h(x) = 7 * 2^(-x), what is the base after simplification?

• 1/2

• 7

• 2

• -1/2

What is the value of f(4) if f(x) = 2^x?

• 2

• 4

• 16

• 8

What does f(0) equal for any exponential function f(x) = a * b^x?

• b

• 1

• 0

• a

If g(x) = 4 * b^x gives a value of 12 when x=1, what is b?

• 12

• 8

• 3

• 4

What type of model is represented by an exponential function with a base greater than 1?

• Linear growth

• Quadratic growth

• Exponential decay

• Exponential growth

What transformation does the function g(x) = 2^(x-1) represent?

• Reflection across the y-axis

• Horizontal shift to the left

• Horizontal shift to the right

• Vertical stretch

What is the effect of the transformation h(x) = 2^(-x) on the graph of f(x) = 2^x?

• Reflection across the x-axis

• Vertical stretch

• Reflection across the y-axis

• Horizontal shift to the right

What does the transformation k(x) = 3 * 2^x do to the graph of f(x) = 2^x?

• Horizontal shift

• Vertical stretch

• Vertical compression

• Reflection