linear vs. Nonlinear relationships

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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 a curve or any other shape that is not linear.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from its equation?

Back

A linear function can be identified by its equation, which will be in the form y = mx + b. If the highest exponent of the variable is 1, it is linear.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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 highest exponent in determining linearity?

Back

The highest exponent in a function's equation determines its degree. A degree of 1 indicates a linear function, while a degree greater than 1 indicates a nonlinear function.

Tags

CCSS.8.F.A.3

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if every vertical line drawn through the graph intersects it at most once. This is known as the vertical line test.

Front

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

Back

A linear equation is an equation that represents a straight line, while a linear function is a specific type of linear equation that defines a relationship between two variables.

Tags

CCSS.8.F.A.3

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as the x-value increases, the y-value decreases.

Tags

CCSS.8.EE.B.5

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is a cubic function?

Back

A cubic function is a nonlinear function of the form y = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.