Functions, Functions, Functions

Front

What is a function?

Back

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

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one x-value is paired with more than one y-value.

Front

How do you determine the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the x-value 1 is paired with two different y-values.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) 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-values) that the function can produce.

Front

What does it mean for a graph to be linear?

Back

A graph is linear if it forms a straight line, indicating a constant rate of change between the x and y values.

Front

What is a linear function?

Back

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