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.

Tags

CCSS.HSF.BF.B.5

Front

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

Back

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

Tags

CCSS.HSF.LE.B.5

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

Front

What is the relationship between logarithmic and exponential functions?

Back

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

Tags

CCSS.HSF.BF.B.5