Linear vs Non-Linear Functions

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 f(x) = 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?

Back

A linear equation can be identified by its standard form, which is Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.

Front

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of the function when x = 0.

Front

What is the general form of a quadratic function?

Back

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

Front

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

Back

A linear function has a constant rate of change and graphs as a straight line, while a quadratic function has a variable rate of change and graphs as a parabola.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where n is a non-negative integer and a_n ≠ 0.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable in the function, which affects the shape and number of roots of its graph.

Front

How do 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 is curved or has bends, the function is nonlinear.