Exponential and Log Flashcard Review

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a * b^x, where a is a constant, b is the base (b > 0, b ≠ 1), and x is the exponent.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases by a constant percentage over a period of time, represented by a function of the form y = a * b^x where b > 1.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases by a constant percentage over a period of time, represented by a function of the form y = a * b^x where 0 < b < 1.

Front

How do you convert a logarithmic equation to its exponential form?

Back

To convert log_b(a) = c to exponential form, use the equation b^c = a.

Front

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

Back

The domain of y = log_b(x) is x > 0, meaning the input must be positive.

Front

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

Back

The range of y = log_b(x) is all real numbers (-∞, ∞).

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

What is the horizontal asymptote of the function f(x) = a * b^x + c?

Back

The horizontal asymptote is y = c.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.