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) + 1?

Back

The asymptote remains at x = 0.

Front

Logarithmic functions are the inverse of which type of functions?

Back

Exponential Functions

Front

What is the general form of a logarithmic function?

Back

y = log_b(x) where b > 0 and b ≠ 1.

Front

What is the value of log₂(8)?

Back

3 (since 2^3 = 8)

Front

What is the value of log₁₀(100)?

Back

2 (since 10^2 = 100)

Front

How does the graph of y = log₅(x + 1) + 1 compare to y = log₅(x)?

Back

It shifts left by 1 unit and up by 1 unit.

Front

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

Back

It changes the steepness of the graph.

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions grow slower than exponential functions.