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

Front

What does the 'a' represent in an exponential function?

Back

The 'a' represents the initial value or y-intercept of the function.

Front

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

Back

The 'b' represents the base of the exponential function, which determines the rate of growth or decay.

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 and 'b' is the base.

Front

How do you identify exponential growth?

Back

Exponential growth occurs when the base 'b' is greater than 1, resulting in the function increasing rapidly as 'x' increases.

Front

How do you identify exponential decay?

Back

Exponential decay occurs when the base 'b' is between 0 and 1, resulting in the function decreasing rapidly as 'x' increases.

Front

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

Back

The y-intercept is 3, which is the value of f(0) = 3(2^0) = 3.

Front

What is the slope in the linear equation y = mx + b?

Back

The slope 'm' represents the rate of change of the function, indicating how much 'y' changes for a unit change in 'x'.

Front

What is the y-intercept in the linear equation y = mx + b?

Back

The y-intercept 'b' is the value of 'y' when 'x' is 0.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases rapidly.