Function Tables

A function table is a chart that shows how each input value relates to an output value based on a specific rule or equation.

It means that for every unit of input, the output will be three times that amount, represented mathematically as $$y = 3x$$ .

To determine the rule, look for a consistent pattern in how the input values change to produce the output values.

A linear function can be expressed in the form $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

The slope represents the rate of change of the output value with respect to the input value.

The output would be $$7(3) + 1 = 22$$ .

The y-intercept is the point where the line crosses the y-axis, representing the output value when the input is zero.

You can verify by substituting the input values into the equation and checking if the output values match those in the table.

This equation represents a linear function where the output increases by 4 for every increase of 1 in the input, starting from 3.

For every unit increase in $$a$$ , $$b$$ increases by 1, starting from 13.