Exponential vs Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a function of the form y = ab^x, where a is a constant, b is a positive real number, and x is the exponent. It grows or decays at a constant percentage rate.

Front

How can you identify a linear function from a graph?

Back

A linear function will show a straight line when graphed, indicating a constant rate of change.

Front

How can you identify an exponential function from a graph?

Back

An exponential function will show a curve that increases or decreases rapidly, indicating a variable rate of change.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the general form of an exponential equation?

Back

The general form of an exponential equation is y = ab^x, where a is a constant and b is the base of the exponential.

Front

What does the slope in a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What does the base in an exponential function represent?

Back

The base represents the growth factor; it indicates how much the function multiplies for each unit increase in x.

Front

If you have $100 and spend $5 every week, what type of function describes your spending?

Back

Linear function: y = -5x + 100.

Front

If you have $5 and triple your money every day, what type of function describes your money growth?

Back

Exponential function.