Characteristics of 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 x-intercept of a function?

Back

The x-intercept of a function is the point where the graph of the function crosses the x-axis, meaning f(x) = 0.

Front

What is the range of an exponential function?

Back

The range of an exponential function f(x) = a * b^x (where a > 0) is (0, ∞) if a is positive, and (-∞, 0) if a is negative.

Front

What does it mean for a function to approach a limit as x approaches negative infinity?

Back

As x approaches negative infinity, the function approaches a specific value, which can indicate horizontal asymptotic behavior.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be horizontal, vertical, or oblique.

Front

How does the base of an exponential function affect its graph?

Back

The base (b) determines the growth rate: if b > 1, the function grows; if 0 < b < 1, the function decays.

Front

What is the vertical shift in an exponential function?

Back

A vertical shift occurs when a constant is added or subtracted from the function, affecting its position on the y-axis.

Front

What is the horizontal shift in an exponential function?

Back

A horizontal shift occurs when a constant is added or subtracted from the x variable, affecting its position on the x-axis.

Front

What is the general form of an exponential function with a vertical shift?

Back

The general form is f(x) = a * b^(x - h) + k, where (h, k) is the point of vertical shift.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept is the value of the function when x = 0, which is f(0) = a, indicating the starting point of the graph.