Linear versus Nonlinear Functions and Review

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. It can include quadratic, exponential, and other types of functions.

Front

How do 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 is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x, often represented as 'm' in the equation y = mx + b.

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, represented by the value of b in the equation y = mx + b.

Front

What is the result of (2⁸)²?

Back

2¹⁶

Front

What is the result of simplifying (4x⁵)²?

Back

16x¹⁰

Front

What is the result of simplifying (3x³y⁵)⁴?

Back

81x¹²y²⁰

Front

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

Back

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

Front

What is the general form of a quadratic function?

Back

A quadratic function is generally in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.