Function Representation and Analysis 8th grade Math

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

How can you determine if a graph represents y as a function of x?

Back

A graph represents y as a function of x if every vertical line intersects the graph at most once (Vertical Line Test).

Front

What is a proportional relationship?

Back

A proportional relationship is one where the ratio between two quantities is constant, and the graph passes through the origin.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant, and the graph does not pass through the origin.

Front

Define the slope of a line.

Back

The slope of a line is the ratio of the change in y to the change in x (rise over run).

Front

What does it mean for a set of ordered pairs to represent y as a function of x?

Back

It means that each x-value in the set is paired with exactly one y-value.

Front

How do you write an equation for distance, speed, and time?

Back

The equation is d = st, where d is distance, s is speed, and t is time.

Front

What is the rate of change in a function?

Back

The rate of change is the amount by which the output (y) changes for a unit change in the input (x).

Front

What is the difference between a table, graph, and equation in representing a function?

Back

A table lists values, a graph visually represents the relationship, and an equation provides a mathematical expression of the relationship.

Front

What is the significance of the origin in a graph?

Back

The origin (0,0) is significant because it is the point where both x and y values are zero, often indicating a starting point in proportional relationships.