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 a positive real number, and 'x' is the exponent.

Front

What is the y-intercept of an exponential function?

Back

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

Front

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

Back

Exponential growth occurs when the value of a function increases at a rate proportional to its current value, typically represented by a base greater than 1 in the function f(x) = a * b^x.

Front

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

Back

Exponential decay occurs when the value of a function decreases at a rate proportional to its current value, typically represented by a base between 0 and 1 in the function f(x) = a * b^x.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of all exponential functions is the x-axis, or y = 0.

Front

How can you identify exponential growth from a function?

Back

If the base 'b' in the function f(x) = a * b^x is greater than 1, the function represents exponential growth.

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How can you identify exponential decay from a function?

Back

If the base 'b' in the function f(x) = a * b^x is between 0 and 1, the function represents exponential decay.

Front

What is the general shape of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises steeply to the right and approaches the horizontal asymptote (x-axis) to the left.

Front

What is the general shape of the graph of an exponential decay function?

Back

The graph of an exponential decay function falls steeply to the right and approaches the horizontal asymptote (x-axis) to the left.

Front

What is the value of f(0) in the function f(x) = 3 * 2^x?

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f(0) = 3 * 2^0 = 3 * 1 = 3.