O4C1 Non-Linear Functions (Exponential Functions)

Front

What is a non-linear function?

Back

A non-linear function is a function that does not create a straight line when graphed. Its rate of change is not constant.

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 does the term 'growth' refer to in exponential functions?

Back

Growth in exponential functions refers to a situation where the function increases rapidly as the value of x increases, typically when the base 'b' is greater than 1.

Front

What does the term 'decay' refer to in exponential functions?

Back

Decay in exponential functions refers to a situation where the function decreases rapidly as the value of x increases, typically when the base 'b' is between 0 and 1.

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph intersects the y-axis, representing the value of the function when x = 0.

Front

How do you identify if a function is linear or exponential from a table of values?

Back

A function is linear if the differences between consecutive y-values are constant. A function is exponential if the ratios of consecutive y-values are constant.

Front

What is the initial value in an exponential function?

Back

The initial value in an exponential function is the y-intercept, which represents the value of the function when x = 0.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where 'a' > 0 and 'b' > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 'a' > 0 and 0 < 'b' < 1.

Front

What does it mean if a graph is not a function?

Back

A graph is not a function if any vertical line drawn through the graph intersects it at more than one point, violating the definition of a function.