Linear and Non-Linear Relationships in Equations, Tables and Graphs

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 non-linear function?

Back

A non-linear function is a function that does not form a straight line when graphed. Its graph can be a curve or any shape that is not a straight line.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are constant, the function is linear.

Front

What does the slope of a linear function represent?

Back

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

Front

What is the y-intercept in a linear equation?

Back

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

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

How can you tell if a graph is 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 quadratic equation?

Back

A linear equation has a degree of 1 and graphs as a straight line, while a quadratic equation has a degree of 2 and graphs as a parabola.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase. This means the graph rises from left to right.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the x-values increase, the y-values decrease. This means the graph falls from left to right.