Functions and Proportional vs. Non-Proportional

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the definition of a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio or rate.

Front

How can you identify if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if no two pairs have the same first element (input) with different second elements (outputs).

Front

What is a y-intercept in a graph?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of y when x is zero.

Front

What does it mean for a relationship to be non-proportional?

Back

A non-proportional relationship does not maintain a constant ratio between the two quantities.

Front

How can you determine if a table of values represents a proportional relationship?

Back

A table represents a proportional relationship if the ratio of y to x is constant for all pairs of values.

Front

What is the difference between a function and a non-function?

Back

A function has a unique output for each input, while a non-function may have multiple outputs for a single input.

Front

What is a mapping in mathematics?

Back

A mapping is a way to describe how each element of one set is paired with an element of another set.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function, representing how much y changes for a unit change in x.

Front

How do you find the slope from a table of values?

Back

To find the slope, calculate the change in y divided by the change in x (rise over run) between two points.