Logarithmic Functions and Their Properties

In this lesson, Kirk Weiler introduces the concept of logarithms, explaining their inverse relationship with exponential functions. The video covers how to graph logarithms by hand, using a table of values, and discusses the domain and range of logarithmic functions. It also demonstrates how to use a calculator to graph and analyze these functions, and explains how to calculate the average rate of change for logarithmic functions.

What is the inverse function of y = 3^x?

• y = x^3

• y = 3x

• y = log base 3 of x

• y = log base x of 3

When graphing y = log base 3 of x, what happens to the coordinates (x, y) from the graph of y = 3^x?

• They are multiplied by 3

• They are switched to (y, x)

• They are divided by 3

• They remain the same

What is the domain of the function y = 3^x?

• x > 0

• x < 0

• All real numbers

• x >= 0

What is the range of the function y = log base 3 of x?

• y > 0

• All real numbers

• y < 0

• y >= 0

Why can't we take the logarithm of a negative number?

• Because it results in a complex number

• Because it results in zero

• Because it results in an undefined value

• Because it results in a negative value

What is the common log?

• log base 2

• log base 10

• log base e

• log base 3

What does the graph of y = log base 10 of x look like near the y-axis?

• It curves away from the y-axis

• It is a straight line

• It approaches but never touches the y-axis

• It intersects the y-axis

If a logarithmic graph is shifted three units to the left, what is the new equation?

• log base 2 of (x - 3)

• log base 2 of (x + 3)

• log base 3 of (x - 3)

• log base 3 of (x + 3)

What must be true about the argument of a logarithmic function?

• It must be less than zero

• It can be any real number

• It must be equal to zero

• It must be greater than zero

What does a small average rate of change in a logarithmic function indicate?

• The function is increasing slowly

• The function is decreasing rapidly

• The function is constant

• The function is increasing rapidly