Graphs of Logarithmic Functions

Front

What is the asymptote of the function \( f(x) = \log_2 x \)?

Back

The asymptote is at \( x = 0 \).

Front

How does the graph of \( g(x) = \log_2(3x + 12) \) compare to \( f(x) = \log_2 x \)?

Back

The graph of \( g(x) \) is translated 4 units left to \( x = -4 \).

Front

What is the inverse of logarithmic functions?

Back

Exponential functions.

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 happens to the graph of \( y = \log(x) \) when you add 4?

Back

The graph shifts up by 4 units, resulting in \( y = \log(x) + 4 \).

Front

What is the range of the function \( f(x) = \log_2 x \)?

Back

The range is \( (-\infty, \infty) \).

Front

What does the base of a logarithm indicate?

Back

The base indicates the number that is raised to a power to obtain a given value.

Front

How do you find the x-intercept of a logarithmic function?

Back

Set the function equal to zero and solve for x.

Front

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

Back

It reflects the graph across the x-axis.

Front

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

Back

The domain is \( (0, \infty) \).