Linear and Exponential Functions From Tables

Front

What is a linear function?

Back

A linear function is a function that can be expressed in the form f(x) = 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 f(x) = a(b)^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 is 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 is the same.

Front

What does the slope of a linear function represent?

Back

The slope 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 of a linear function represent?

Back

The y-intercept is the value of y when x = 0, indicating where the line crosses the y-axis.

Front

What is the significance of the base in an exponential function?

Back

The base determines the growth or decay rate of the function; if b > 1, the function grows, and if 0 < b < 1, the function decays.

Front

How do you convert a table of values into a linear function?

Back

Identify the slope (m) and y-intercept (b) from the table, then use the formula f(x) = mx + b.

Front

How do you convert a table of values into an exponential function?

Back

Identify the initial value (a) and the growth factor (b) from the table, then use the formula f(x) = a(b)^x.

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.