Practice: Characteristics of Log Graphs

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.

Front

What does the graph of a logarithmic function look like?

Back

The graph of a logarithmic function is a curve that increases slowly and approaches the vertical line (asymptote) but never touches it.

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 x = 0.

Front

How do transformations affect the graph of a logarithmic function?

Back

Transformations such as shifts and reflections can change the position and orientation of the graph. For example, y = log_b(x - h) + k shifts the graph right by h and up by k.

Front

What is the effect of shifting a logarithmic graph to the right?

Back

Shifting a logarithmic graph to the right by h units means the function will start at x = h instead of x = 0.

Front

What is the effect of shifting a logarithmic graph down?

Back

Shifting a logarithmic graph down by k units lowers the entire graph by k, affecting the y-values.

Front

How do you identify the asymptote of a logarithmic function?

Back

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

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverse of exponential functions. If y = log_b(x), then x = b^y.

Front

What does the notation log_b(x) mean?

Back

log_b(x) represents the logarithm of x to the base b, which answers the question: 'To what power must b be raised to obtain x?'