Linear vs Exponential 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. The graph of an exponential function increases or decreases rapidly.

Front

How can you identify a linear function from a graph?

Back

A linear function will show a constant rate of change, represented by a straight line on a graph.

Front

How can you identify an exponential function from a graph?

Back

An exponential function will show a rapid increase or decrease, represented by a curve that gets steeper or shallower.

Front

What is the slope in a linear function?

Back

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

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept (b) is the value of y when x is 0, representing the point where the line crosses the y-axis.

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 much larger values over time.

Front

If a function doubles every hour, what type of function is it?

Back

It is an exponential function, as it grows by a constant factor (doubling) over equal intervals.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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 the initial value and b is the growth factor.