Writing and interpreting functions

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the constant amount by which the function's output (y) changes for a unit change in the input (x). It is often represented as the slope (m) in the equation y = mx + b.

Front

How do you calculate the average rate of change between two points?

Back

The average rate of change between two points (x1, y1) and (x2, y2) is calculated using the formula: (y2 - y1) / (x2 - x1).

Front

What does a rate of change of 0 indicate about a function?

Back

A rate of change of 0 indicates that the function is constant over the interval, meaning there is no change in the output value as the input value changes.

Front

What does a positive rate of change indicate?

Back

A positive rate of change indicates that as the input value increases, the output value also increases.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as the input value increases, the output value decreases.

Front

What is the significance of the slope in a linear function?

Back

The slope of a linear function represents the rate of change of the function. It indicates how steep the line is and the direction of the change.

Front

What is an undefined rate of change?

Back

An undefined rate of change occurs when the change in the x-values is zero, which typically happens in vertical lines where the slope cannot be calculated.

Front

How can you determine if a function is linear?

Back

A function is linear if it can be represented by a straight line on a graph, which means it has a constant rate of change.

Front

What is the formula for the slope of a line?

Back

The formula for the slope (m) of a line is m = (y2 - y1) / (x2 - x1).

Front

What does it mean for a function to have a non-constant slope?

Back

A function with a non-constant slope is non-linear, meaning the rate of change varies at different points along the function.