Exponential Function Review

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

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, 'b' is the base, and 'x' is the exponent.

Front

What does the base 'b' in an exponential function represent?

Back

The base 'b' represents the growth factor of the function. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

How do you find the value of an exponential function at a specific point?

Back

To find f(c) for a function f(x) = a * b^x, substitute 'c' into the function: f(c) = a * b^c.

Front

What is the range of the function f(x) = a * b^x?

Back

The range is (0, ∞) if a > 0, and (-∞, 0) if a < 0.

Front

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

Back

The initial value is 3, which is the value of the function when x = 0.

Front

What transformation occurs in the function f(x) = 3^x + 2 compared to the parent function f(x) = 3^x?

Back

The function is shifted 2 units up.

Front

What is the y-intercept of the function f(x) = 3 * 2^x?

Back

The y-intercept is the initial value, which is 3, when x = 0.

Front

How does the graph of an exponential function behave as x approaches infinity?

Back

As x approaches infinity, the value of f(x) approaches infinity for b > 1, indicating exponential growth.

Front

How does the graph of an exponential function behave as x approaches negative infinity?

Back

As x approaches negative infinity, the value of f(x) approaches 0, indicating that the function approaches the x-axis but never touches it.