AB PrecCalc Log Graphs/Exp Graphs

Front

What is the general form of an exponential function?

Back

y = a * b^x, where a is a constant, b is the base, and x is the exponent.

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. For example, in log_b(x), b is the base.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions are the inverse of logarithmic functions. If y = b^x, then x = log_b(y).

Front

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

Back

The domain is (0, ∞) because logarithms are only defined for positive real numbers.

Front

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

Back

The range is (-∞, ∞) because logarithmic functions can take any real value.

Front

How do you find the inverse of a function?

Back

To find the inverse, swap the x and y variables and solve for y.

Front

What is the effect of a vertical shift on the graph of an exponential function?

Back

A vertical shift moves the graph up or down without changing its shape. For example, y = 2^x + 3 shifts the graph of y = 2^x up by 3 units.

Front

What is the effect of a horizontal shift on the graph of a logarithmic function?

Back

A horizontal shift moves the graph left or right. For example, f(x) = log_2(x - 1) shifts the graph of f(x) = log_2(x) to the right by 1 unit.

Front

What does it mean for a function to be invertible?

Back

A function is invertible if it passes the horizontal line test, meaning each y-value corresponds to exactly one x-value.

Front

What is the horizontal asymptote of the function y = 2^x?

Back

The horizontal asymptote is y = 0, as the function approaches 0 but never reaches it as x approaches negative infinity.