Comparing Functions

Front

What is the rate of change in a function?

Back

The rate of change in a function describes how much the output value (y) changes for a change in the input value (x). It is often represented as the slope in linear functions.

Front

How do you determine who has a greater rate of change between two functions?

Back

To determine who has a greater rate of change, compare the slopes of the functions. The function with the higher slope value has the greater rate of change.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its rate of change varies and can be represented by equations such as y = ax^2 + bx + c.

Front

What is the slope of the line represented by the equation y = 4x + 6?

Back

The slope of the line is 4.

Front

What is the slope of the line represented by the equation y = 7x^3 + 5?

Back

The slope is not constant; it varies depending on the value of x, indicating it is a nonlinear function.

Front

How can you identify a linear function from its equation?

Back

A linear function can be identified by its equation being in the form y = mx + b, where m and b are constants.

Front

What does it mean if two functions have the same rate of change?

Back

If two functions have the same rate of change, it means they have the same slope and will be parallel lines when graphed.

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 value when the input value (x) is zero.

Front

How do you find the rate of change from a table of values?

Back

To find the rate of change from a table of values, calculate the difference in the output values (y) divided by the difference in the input values (x) for two points.