Exponential and Logarithmic Graphs

Front

What is the domain of exponential and logarithmic functions?

Back

The domain of exponential functions is (-∞, ∞) and the domain of logarithmic functions is (0, ∞).

Front

What is the range of exponential and logarithmic functions?

Back

The range of exponential functions is (0, ∞) and the range of logarithmic functions is (-∞, ∞).

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^(x - h) + k, where a is a vertical stretch, b is the base, (h, k) is the vertex.

Front

What is the general form of a logarithmic function?

Back

The general form of a logarithmic function is f(x) = a * log_b(x - h) + k, where a is a vertical stretch, b is the base, and (h, k) is the vertex.

Front

What does it mean for a function to be reflected over the x-axis?

Back

A function is reflected over the x-axis when all y-values are multiplied by -1, resulting in a vertical flip of the graph.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches ±∞.

Front

Which type of function has a horizontal asymptote?

Back

Exponential functions have a horizontal asymptote.

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.718.

Front

How do you convert between exponential and logarithmic forms?

Back

To convert from exponential form a^b = c to logarithmic form, use log_a(c) = b.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number.