Exponential Graphs

Front

What is an exponential function?

Back

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

Front

What does the base of an exponential function determine?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function y = a(b^x) is the point where x = 0, which is (0, a).

Front

How do you identify exponential growth on a graph?

Back

Exponential growth is identified on a graph by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

Front

How do you identify exponential decay on a graph?

Back

Exponential decay is identified on a graph by a curve that falls steeply as x increases, indicating that the function's value decreases rapidly.

Front

What is the general form of an exponential growth equation?

Back

The general form of an exponential growth equation is y = a(b^x) where b > 1.

Front

What is the general form of an exponential decay equation?

Back

The general form of an exponential decay equation is y = a(b^x) where 0 < b < 1.

Front

What is the significance of the constant 'a' in an exponential function?

Back

The constant 'a' in an exponential function represents the initial value or the y-intercept of the function.

Front

What is the effect of changing the base 'b' in an exponential function?

Back

Changing the base 'b' affects the steepness of the graph. A larger base results in a steeper curve for growth, while a smaller base (greater than 1) results in a less steep curve.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, (-∞, ∞).