Practice: Characteristics of Log Graphs

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 does the base of a logarithm indicate?

Back

The base of a logarithm indicates the number that is raised to a power to obtain a given number. For example, log_b(x) = y means b^y = x.

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is all positive real numbers (x > 0).

Front

What is the range of a logarithmic function?

Back

The range of a logarithmic function is all real numbers (-∞, ∞).

Front

What is an asymptote in the context of logarithmic graphs?

Back

An asymptote is a line that the graph approaches but never touches. For logarithmic functions, the vertical asymptote is typically at x = 0.

Front

How does a vertical shift affect the graph of a logarithmic function?

Back

A vertical shift moves the graph up or down. For example, y = log_b(x) + k shifts the graph up by k units.

Front

How does a horizontal shift affect the graph of a logarithmic function?

Back

A horizontal shift moves the graph left or right. For example, y = log_b(x - h) shifts the graph right by h units.

Front

What is the effect of a negative sign in front of a logarithmic function?

Back

A negative sign reflects the graph across the x-axis. For example, y = -log_b(x) flips the graph upside down.

Front

What does the transformation y = log_b(x - h) + k represent?

Back

This transformation represents a horizontal shift to the right by h units and a vertical shift up by k units.

Front

How do you identify the vertical asymptote of a logarithmic function?

Back

The vertical asymptote can be found by setting the argument of the logarithm to zero. For y = log_b(x - h), the asymptote is at x = h.