Characteristics 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.

Tags

CCSS.HSF.BF.B.5

Front

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

Back

The domain of f(x) = log_b(x) is x > 0.

Front

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

Back

The range of f(x) = log_b(x) is all real numbers (-∞, ∞).

Front

Describe the end behavior of the function y = log_b(x).

Back

As x approaches 0 from the right, y approaches -∞; as x approaches ∞, y approaches ∞.

Tags

CCSS.HSF-IF.C.7E

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

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

Back

To convert log_b(x) = y to exponential form, rewrite it as b^y = x.

Tags

CCSS.HSF.BF.B.5

Front

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

Back

The vertical asymptote is at x = 0.

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

Front

What is the value of log_b(b)?

Back

The value of log_b(b) is 1.