Graphing Logarithmic Functions

Front

What is the general form of a logarithmic function?

Back

y = log_b(x) where b is the base of the logarithm.

Front

What is the relationship between logarithmic functions and exponential functions?

Back

Logarithmic functions are the inverse of exponential functions.

Front

How do you find the domain of a logarithmic function?

Back

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

Front

What is the range of a logarithmic function?

Back

The range of a logarithmic function is all real numbers.

Front

How do you determine the vertical asymptote of a logarithmic function?

Back

The vertical asymptote of y = log_b(x - h) + k is x = h.

Front

What does the base of a logarithm indicate?

Back

The base of a logarithm indicates the number that is raised to a power to obtain a given number.

Front

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

Back

If y = log_b(x), then it can be rewritten as b^y = x.

Front

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

Back

Changing the base of a logarithm affects the steepness and position of the graph.

Front

What is the significance of the point (1,0) on the graph of a logarithmic function?

Back

The point (1,0) indicates that log_b(1) = 0 for any base b.

Front

How do you graph a logarithmic function?

Back

To graph a logarithmic function, identify the vertical asymptote, plot key points, and determine the end behavior.