Graphs of Logarithmic Functions

Front

What is a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, typically expressed as y = 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 is the domain of a logarithmic function?

Back

The domain of a logarithmic function is (0, ∞), meaning it only accepts positive real numbers.

Front

What is the range of a logarithmic function?

Back

The range of a logarithmic function is (-∞, ∞), meaning it can take any real number as its output.

Front

How do you graph a logarithmic function?

Back

To graph a logarithmic function, plot points for various x values, noting that the graph will pass through (1,0) and approach the vertical asymptote at x=0.

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverse of exponential functions, meaning if y = log_b(x), then x = b^y.

Front

What does the graph of y = log_b(x) look like?

Back

The graph of y = log_b(x) is a curve that increases slowly, passing through (1,0) and approaching the y-axis but never touching it.

Front

What happens to the graph of a logarithmic function when the base increases?

Back

As the base of a logarithmic function increases, the graph becomes steeper, indicating that the function grows faster.

Front

What is the effect of adding a constant to a logarithmic function?

Back

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

Front

What is the effect of subtracting a constant from a logarithmic function?

Back

Subtracting a constant from a logarithmic function, such as y = log_b(x) - k, shifts the graph vertically down by k units.