Graphing 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 inverse of the logarithmic function y = log_b(x)?

Back

The inverse is the exponential function x = b^y.

Front

What is the general shape of a logarithmic function graph?

Back

The graph of a logarithmic function increases slowly and has a vertical asymptote.

Front

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

Back

The domain is x > 0.

Front

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

Back

The range is all real numbers.

Front

What does the vertical asymptote of a logarithmic function represent?

Back

The vertical asymptote represents the value of x where the function is undefined, typically at x = 0.

Front

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

Back

Set y = 0 and solve for x in the equation log_b(x) = 0, which gives x = 1.

Front

What is the effect of changing the base of a logarithm?

Back

Changing the base affects the steepness of the graph but not the overall shape.

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverses of exponential functions, meaning they undo each other.