8.9 Graphing Logarithmic Functions

Front

What is the base of a logarithmic function?

Back

The base of a logarithmic function is the number that is raised to a power to obtain a given value. For example, in log_b(x), b is the base.

Front

Which function has a vertical asymptote?

Back

Logarithmic functions have a vertical asymptote at the value of x where the function is undefined, typically at x = 0.

Front

How are exponentials and logarithms related?

Back

Exponentials and logarithms are inverse functions. If y = b^x, then x = log_b(y).

Front

What is the domain of log(x)?

Back

The domain of log(x) is (0, ∞), meaning it is defined for all positive real numbers.

Front

What is the range of logarithmic functions?

Back

The range of logarithmic functions is (-∞, ∞), meaning they can take any real number as an output.

Front

What does log_b(x) represent?

Back

log_b(x) represents the exponent to which the base b must be raised to produce the number x.

Front

What is the value of log_10(100)?

Back

The value of log_10(100) is 2, because 10^2 = 100.

Front

What is the relationship between log_b(b) and 1?

Back

log_b(b) = 1, because any number raised to the power of 1 is itself.

Front

What is the value of log_5(25)?

Back

The value of log_5(25) is 2, because 5^2 = 25.

Front

What is the change of base formula for logarithms?

Back

The change of base formula is log_b(a) = log_k(a) / log_k(b), where k is any positive number.