Logarithmic Transformations

Front

What is the domain of the function f(x) = log₂(x)?

Back

Domain: x > 0

Front

What is the range of the function f(x) = log₂(x)?

Back

Range: all real numbers

Front

What happens to the asymptote of y = log₂(x + 2)?

Back

The asymptote shifts left two to x = -2.

Front

What is the equation of the asymptote for the function y = log₂(x + 3)?

Back

x = -3

Front

What are the transformations of the graph of y = log₂(x) + 5?

Back

Up 5

Front

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

Back

It shifts the graph vertically.

Front

What is the effect of subtracting a constant from the input of a logarithmic function?

Back

It shifts the graph horizontally.

Front

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

Back

Set the argument of the log function to zero.

Front

What is the general form of a logarithmic function?

Back

y = log_b(x - h) + k, where (h, k) is the shift.

Front

What is the base of the logarithm in the function y = log₅(x)?

Back

Base: 5