Graphing Exponential Functions: Key Concepts and Examples

This video tutorial covers exponential functions, including their identification, evaluation, and graphing. It explains how to distinguish between linear and exponential functions, evaluate them for specific x values, and graph them while comparing to parent functions. The tutorial also explores transformations of exponential functions and their applications in real-world scenarios, such as modeling bacterial growth.

What is the base condition for 'b' in an exponential function?

• b must equal 0

• b must be less than 0

• b must not equal 1

• b must be greater than 1

In the function y = 3 * 0.5^(-2), what does the negative exponent indicate?

• The function is undefined

• The function has no solution

• The base should be reciprocated

• The base is negative

What is the y-intercept of the function y = 4 * 2^x?

• 16

• 2

• 4

• 8

How does multiplying an exponential function by a constant affect its graph?

• No change

• Horizontal shift

• Vertical stretch

• Reflection on the x-axis

What is the domain of any exponential function?

• All positive numbers

• All negative numbers

• Only integers

• All real numbers

What does a vertical translation in the graph of an exponential function indicate?

• Change in the exponent's sign

• Shift along the x-axis

• Change in the base of the function

• Shift along the y-axis

In the function y = 4 * 2^(x - 3) + 2, what does 'x - 3' in the exponent suggest?

• Horizontal shift to the left

• Vertical shift

• Horizontal shift to the right

• No shift

What is the range of the function y = 4 * 2^(x - 3) + 2?

• y > 0

• y > 2

• y > 4

• y < 2

How does the function y = 3 * 1.5^x model growth?

• Exponential growth

• Linear growth

• Quadratic growth

• Logarithmic growth

What is the value of y when x = 0.5 in the function y = 3 * 4^x?

• 6

• 12

• 18

• 24