Linear or Nonlinear

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 it can take various forms such as quadratic, exponential, or logarithmic.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

How can you determine if a function is linear or nonlinear from its graph?

Back

If the graph is a straight line, the function is linear. If the graph curves or has bends, the function is nonlinear.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

If a function has a constant rate of change, what type of function is it?

Back

If a function has a constant rate of change, it is a linear function.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as x increases, y also increases. This is typically represented by a positive slope.