Relations, Functions with Domain/Range, Rate Change , Dir Var

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y) that the function can produce.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input (x) is associated with exactly one output (y). This can be checked using the vertical line test.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, then the relation is not a function.

Front

What is the rate of change in a function?

Back

The rate of change is a measure of how much the output (y) changes for a given change in the input (x). It is often calculated as the change in y divided by the change in x.

Front

Calculate the rate of change for the function f(x) = 2x + 3 between x = 1 and x = 3.

Back

The rate of change is (f(3) - f(1)) / (3 - 1) = (9 - 5) / 2 = 2.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

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

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 a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y).