Flashcard Review: Key Features of Log Functions

Front

What is the range of the logarithmic function?

Back

The range of a logarithmic function is \( (-\infty, \infty) \).

Front

What is an asymptote in the context of logarithmic functions?

Back

An asymptote is a line that the graph approaches but never touches. For logarithmic functions, the vertical asymptote is typically at the x-value where the function is undefined.

Front

Describe the transformation of the function \( y=\log_2(x+1)-3 \) from the parent function \( y=\log_2(x) \).

Back

The transformation is left 1 unit and down 3 units.

Front

Calculate \( \log_3(81) \).

Back

\( \log_3(81) = 4 \) because \( 3^4 = 81 \).

Front

What is the base of the logarithm in the function \( y=\log_4(x) \)?

Back

The base of the logarithm is 4.

Front

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

Back

The domain is \( (0, \infty) \), meaning x must be greater than 0.

Front

What does the graph of a logarithmic function look like?

Back

The graph of a logarithmic function increases slowly and has a vertical asymptote at the x-axis.

Front

What is the value of \( \log_{10}(100) \)?

Back

\( \log_{10}(100) = 2 \) because \( 10^2 = 100 \).

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. For example, if \( b^y = x \), then \( \log_b(x) = y \).

Front

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

Back

Changing the base of a logarithm affects the steepness of the graph but not the overall shape.