Logarithm Graphs

Front

What is a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, typically expressed as f(x) = log_b(x), where b is the base.

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. For example, in log_b(x), b is the base.

Front

What does the graph of a logarithmic function look like?

Back

The graph of a logarithmic function increases slowly and has a vertical asymptote at x = 0.

Front

What is the transformation of f(x) = log_b(x - h) + k?

Back

The graph shifts right by h units and up by k units.

Front

What is the horizontal asymptote of the function f(x) = log_b(x)?

Back

The horizontal asymptote is y = 0.

Front

How do you find the x-intercept of a logarithmic function?

Back

Set f(x) = 0 and solve for x.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms answer the question: 'To what exponent must the base be raised to produce a given number?'

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is x > 0.

Front

What is the range of a logarithmic function?

Back

The range of a logarithmic function is all real numbers.

Front

What is the effect of a negative coefficient in front of a logarithmic function?

Back

It reflects the graph across the x-axis.