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 graph can be curved or have varying slopes.

Front

How can you identify a linear equation from its standard form?

Back

A linear equation in standard form is typically written as Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

The slope (m) in a linear function indicates the rate of change of the function; it represents how much y changes for a unit change in x.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept (b) in a linear function is the point where the graph intersects the y-axis, indicating the value of y when x = 0.

Front

Can a linear function have a variable exponent?

Back

No, a linear function cannot have a variable exponent; the exponent of the variable must be 1.

Front

What is the difference between a linear and a quadratic function?

Back

A linear function has a constant rate of change and is represented by a straight line, while a quadratic function has a variable rate of change and is represented by a parabola.

Front

What is a common example of a nonlinear function?

Back

A common example of a nonlinear function is a quadratic function, such as y = x^2.

Front

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

Back

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