Graphing Exponential Functions

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 of the exponential (b > 0, b ≠ 1), and 'x' is the exponent.

Front

What is the general form of an exponential growth function?

Back

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

Front

What is the general form of an exponential decay function?

Back

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

Front

How can you determine if a function represents exponential growth or decay?

Back

If the base 'b' in the function y = a(b^x) is greater than 1, it represents exponential growth. If 'b' 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 (0, a), which is the value of the function when x = 0.

Front

How do you find the y-intercept of the function y = 3^x?

Back

To find the y-intercept, substitute x = 0 into the function: y = 3^0 = 1. Thus, the y-intercept is (0, 1).

Front

What is the significance of the y-intercept in exponential functions?

Back

The y-intercept indicates the initial value of the function when x = 0, which is crucial for understanding the function's behavior.

Front

What does the point (0, 6) represent in the context of an exponential function?

Back

The point (0, 6) represents the y-intercept of the exponential function, indicating that when x = 0, the value of the function is 6.

Front

What is an example of an increasing exponential function?

Back

An example of an increasing exponential function is y = 50(1.4^x), where the base 1.4 is greater than 1.

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 faster growth over time.