8.9 Graphing Logarithmic Functions

Front

What is a logarithmic function?

Back

A logarithmic function is the inverse of an exponential function, typically written 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 vertical asymptote of a logarithmic function?

Back

The vertical asymptote of a logarithmic function is a vertical line that the graph approaches but never touches, typically at x = 0.

Tags

CCSS.HSF-IF.C.7E

Front

What is the range of a logarithmic function?

Back

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

Tags

CCSS.HSF-IF.C.7E

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

How do you graph a logarithmic function?

Back

To graph a logarithmic function, plot points for various x values, draw the vertical asymptote at x = 0, and ensure the curve increases without bound.

Tags

CCSS.HSF-IF.C.7E

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential and logarithmic functions are inverses of each other; if y = b^x, then x = log_b(y).

Tags

CCSS.HSF.BF.B.5

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

Which function has a horizontal asymptote?

Back

Exponential functions have a horizontal asymptote, typically at y = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What happens to the value of log(x) as x approaches 0 from the right?

Back

As x approaches 0 from the right, log(x) approaches -∞.

Tags

CCSS.HSF-IF.C.7E