Logarithmic and Exponential Functions

The video covers exponential functions, including their general form, properties, and graphing techniques. It explains exponential growth and decay, introduces logarithms, and discusses their properties and how to solve logarithmic equations. Examples and practice problems are provided throughout to reinforce learning.

What is the domain of an exponential function in the form y = a * b^(x-c) + d?

• y > d

• x < c

• x > c

• All real numbers

If the base of an exponential function is greater than 1, what type of behavior does the function exhibit?

• Growth

• Constant

• Decay

• Oscillation

What is the approximate value of the Euler number 'e'?

• 3.14

• 2.718

• 1.618

• 1.414

In the compound interest formula, what does 'P' represent?

• Number of times compounded

• Time in years

• Interest rate

• Principal amount

How is a logarithmic function related to an exponential function?

• They are inverses of each other

• They are the same

• They are unrelated

• They are both linear

What is the domain of a logarithmic function y = log_b(x-c) + d?

• y > d

• y < d

• x < c

• x > c

Which property of logarithms allows you to express log_b(m*n) as a sum?

• Inverse property

• Power property

• Quotient property

• Product property

What is the result of log_b(b^x)?

• b

• 0

• x

• 1

How can you express log_b(m/n) using logarithmic properties?

• log_b(m^n)

• log_b(m*n)

• log_b(m) - log_b(n)

• log_b(m) + log_b(n)

What is the power property of logarithms?

• log_b(m^n) = n * log_b(m)

• log_b(m*n) = log_b(m) + log_b(n)

• log_b(m/n) = log_b(m) - log_b(n)

• log_b(1) = 0