Function and Relation Flashcard

Front

What is a function?

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 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 does it mean for y to be a function of x?

Back

It means that for each value of x, there is exactly one corresponding value of y.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

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

Back

A linear function will have a constant rate of change; the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax^2 + bx + c, which graphs as a parabola.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the value of f(x) also increases.

Front

What is a table of values?

Back

A table of values is a way to organize pairs of input (x) and output (y) values to analyze the relationship between them.