Graphing Logarithmic Functions with Transformations

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches or crosses, indicating that the function approaches infinity or negative infinity as it nears the asymptote.

Front

Which function has a vertical asymptote: Exponential or Logarithmic?

Back

Logarithmic functions have a vertical asymptote.

Front

What is the general form of a logarithmic function?

Back

The general form is y = log_b(x - h) + k, where (h, k) is the translation of the graph.

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 value.

Front

How does the graph of y = log_b(x) behave as x approaches 0?

Back

As x approaches 0 from the right, y approaches negative infinity.

Front

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

Back

A horizontal shift to the right by h units.

Front

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

Back

A vertical shift upward by k units.

Front

What does a negative sign in front of a logarithmic function indicate?

Back

It indicates a reflection over the x-axis.

Front

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

Back

The vertical asymptote is found at x = h in the function y = log_b(x - h).

Front

What is the effect of adding a constant to a logarithmic function?

Back

Adding a constant shifts the graph vertically.