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 in y-values divided by the difference in x-values is the same for all intervals.

Front

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

Back

An exponential function will have a constant ratio of successive y-values, meaning each y-value is a constant multiple of the previous one.

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 base of an exponential function represent?

Back

The base represents the growth factor; it indicates how much the function value increases (if greater than 1) or decreases (if between 0 and 1) for each unit increase in x.

Front

Write the function for the following table: (1, 5), (2, 9), (3, 13).

Back

f(x) = 4x + 1.

Front

Write the function for the following table: (0, 1), (1, 2), (2, 4).

Back

f(x) = 1(2)^x.

Front

Write the function for the following table: (0, 1), (1, 3), (2, 9).

Back

f(x) = 1(3)^x.

Front

Write the function for the following table: (0, 27), (1, 9), (2, 3).

Back

f(x) = 27(1/3)^x.