Linear vs Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 in which an independent variable appears in the exponent. It has the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change, meaning the difference between consecutive y-values divided by the difference in x-values will be the same.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will have a constant ratio of change, meaning the ratio of consecutive y-values divided by the ratio of consecutive x-values will be the same.

Front

What does the slope of 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 y-intercept of a linear function represent?

Back

The y-intercept is the value of y when x is 0; it represents the starting point of the function on the y-axis.

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 a constant, b is the base, and x is the exponent.

Front

What type of function is represented by the equation y = -3x + 12?

Back

Linear.

Front

What type of function is represented by the equation y = 2(3^x)?

Back

Exponential.