Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will show a constant ratio between consecutive values, meaning that as x increases, the y-values increase by a consistent multiplicative factor.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where a is the initial value and b is the growth (b > 1) or decay (0 < b < 1) factor.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, represented by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much faster growth over time.

Front

What is a common base for exponential functions?

Back

The most common bases for exponential functions are 2 (binary growth), e (natural growth), and 10 (common logarithmic growth).

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the value of f(0), which equals a.

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How do you determine if a function is exponential from a graph?

Back

An exponential function will show a curve that rises or falls sharply, rather than a straight line, indicating rapid growth or decay.

Front

What is the domain and range of an exponential function?

Back

The domain of an exponential function is all real numbers (-∞, ∞), and the range is all positive real numbers (0, ∞).

Front

What is exponential decay?

Back

Exponential decay occurs when the base of the exponential function is between 0 and 1 (0 < b < 1), resulting in a decrease in value as x increases.