Log Transformations

Front

What is a log transformation?

Back

A log transformation is a mathematical operation that replaces a variable with its logarithm, often used to stabilize variance and make data more normally distributed.

Front

What is the parent function of a logarithmic function?

Back

The parent function of a logarithmic function is y = log_b(x), where b is the base of the logarithm.

Front

How does the graph of y = log_b(x) behave as x approaches 0?

Back

As x approaches 0 from the right, y approaches negative infinity, indicating a vertical asymptote at x = 0.

Front

What effect does adding a constant to a logarithmic function have?

Back

Adding a constant to a logarithmic function, such as y = log_b(x) + k, shifts the graph vertically by k units.

Front

What does the equation y = log_b(x - h) represent?

Back

This equation represents a horizontal shift of the logarithmic function to the right by h units.

Front

What is the effect of multiplying a logarithmic function by a constant?

Back

Multiplying a logarithmic function by a constant, such as y = k * log_b(x), results in a vertical stretch or compression depending on the value of k.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number, denoted as log_b(a) = c, meaning b^c = a.

Front

How do you convert a logarithmic equation to an exponential form?

Back

To convert log_b(a) = c to exponential form, use the equation b^c = a.

Front

What is the domain of the logarithmic function y = log_b(x)?

Back

The domain of the logarithmic function y = log_b(x) is x > 0.

Front

What is the range of the logarithmic function y = log_b(x)?

Back

The range of the logarithmic function y = log_b(x) is all real numbers.