Graphs of Logarithms

Front

What is the general form of a logarithmic function?

Back

f(x) = log_b(x) where b > 0 and b ≠ 1.

Front

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

Back

Domain: x > 0.

Front

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

Back

Range: all real numbers.

Front

What transformation occurs when you add a constant to a logarithmic function?

Back

It translates the graph vertically.

Front

What transformation occurs when you subtract a constant from the input of a logarithmic function?

Back

It translates the graph horizontally.

Front

What is the vertical asymptote of the function f(x) = log(x)?

Back

Vertical asymptote: x = 0.

Front

How do you find the equation of the asymptote for f(x) = log(x + c)?

Back

Set the argument of the log to zero: x + c = 0, so x = -c.

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 base of the natural logarithm?

Back

The base of the natural logarithm is e (approximately 2.718).

Front

How do you express the logarithm of a product?

Back

log_b(m * n) = log_b(m) + log_b(n).