11/26 makeup (Set #2) 8.15 - Rel, Funct, Domain and Range

Front

What is the range of a graph?

Back

The range of a graph is the set of all possible output values (y-values) that the function can produce. For example, if the range is y≥1, it means the graph only produces values of y that are greater than or equal to 1.

Front

What does it mean for a graph to pass the vertical line test?

Back

A graph passes the vertical line test if no vertical line intersects the graph at more than one point. This indicates that the relation represented by the graph is a function.

Front

What is a function?

Back

A function is a relation where each input (x-value) is associated with exactly one output (y-value). For example, the relation {(1,-5), (2,3), (3,1)} is a function because each x-value is unique.

Front

What is the domain of a relation?

Back

The domain of a relation is the set of all possible input values (x-values) that can be used in the function. For example, for the relation {(-4, 3), (2, 1), (0, 3), (-3, -2)}, the domain is xE{-4, -3, 0, 2}.

Front

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

Back

A function has unique outputs for each input, while a non-function can have multiple outputs for the same input. For example, the relation {(1,-5), (-1,6), (1,5), (6,-3)} is not a function because the input 1 has two different outputs (-5 and 5).

Front

How do you determine the range of a graph?

Back

To determine the range of a graph, identify the lowest and highest y-values that the graph reaches. For example, if a graph only reaches y-values starting from 1 and going upwards, the range is y≥1.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, written as (x, y). For example, (2, 3) represents a point where x=2 and y=3.

Front

What does it mean if a graph has a range of -3 ≤ y < 1?

Back

This means that the y-values of the graph start at -3 and go up to, but do not include, 1. The graph can take any value between -3 and 1, including -3 but not 1.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line drawn on the graph intersects it at more than one point, then the graph does not represent a function.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output. For example, the relation {(1,2), (2,3), (3,4)} shows how each input is related to an output.