HW #33 - Rate of Change

Front

What is a function?

Back

A function is a relation where each input has exactly one output.

Front

What is the definition of rate of change?

Back

Rate of change is a measure of how much a quantity changes in relation to another quantity.

Front

How do you determine if a mapping is a function?

Back

A mapping is a function if every input corresponds to exactly one output.

Front

What does a constant slope indicate in a graph?

Back

A constant slope indicates a linear relationship between the variables.

Front

What is a non-linear relationship?

Back

A non-linear relationship is one where the rate of change is not constant, resulting in a curve on a graph.

Front

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

Back

Rate of change = (change in y) / (change in x).

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope is 2.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as one quantity increases, the other quantity decreases.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in a linear function?

Back

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