Graphing Logarithmic Functions

Front

What is the equation of the asymptote for the function y = log_b(x - h) + k?

Back

The equation of the vertical asymptote is x = h.

Front

What is the domain of the function f(x) = log_b(x + 1)?

Back

The domain is D: (−1, ∞).

Front

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

Back

The range is R: (−∞, ∞).

Front

What does the graph of y = -log_b(x) look like?

Back

It is a reflection of the graph of y = log_b(x) across the x-axis.

Front

What is the vertical asymptote of the function y = log_b(x - 4)?

Back

The vertical asymptote is at x = 4.

Front

How do you find the x-intercept of the function y = log_b(x)?

Back

Set y = 0 and solve for x: 0 = log_b(x) implies x = 1.

Front

What is the effect of the '+ k' in the function y = log_b(x) + k?

Back

It shifts the graph vertically by k units.

Front

What is the effect of the '- h' in the function y = log_b(x - h)?

Back

It shifts the graph horizontally to the right by h units.

Front

What is the domain of the function f(x) = -ln(x - 2) + 3?

Back

The domain is D: (2, ∞).

Front

What is the range of the function f(x) = -ln(x - 2) + 3?

Back

The range is R: (-∞, 3).