Prentice Hall's Online Lesson Quiz Enter Web Code: aga–0201
Cartesian Coordinate Plane |
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The Cartesian Coordinate plane is composed of the x-axis (horizontal) and the y-axis (vertical), which meet at the origin (0,0) and divide the plane into four quadrants. Ordered pairs graphed on the plane can be represented by (x,y). |
A relation is a set of ordered pairs.
The domain of a relation is the set of
all x-coordinates. In the example above the domain is:
D: {4, –2, 5, 0}
The range of a relation is the set of all
y-coordinates. In the example above the range is
R: {5, 1, 6, 2}
A relation can be shown by a mapping, a graph, equations, or a list (table).
Mapping
A mapping shows how each member of the domain is paired with each member of the range.
A function is a special type of relation.
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By definition, a function exists if and only if every element of the domain is paired with exactly one element from the range. |
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That is, for every x-coordinate there is exactly one y-coordinate. |
| All functions are relations, but not all relations are functions. |
A: {(4,5), (–2,1), (5,6), (0,2)}
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Set A is a function, every
member of the domain pairs with exactly one member of the range. |
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B: {(4,5), (–2,1), (4,6), (0,2)}
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Set B is not a function,
since the 4 in the domain pairs with both 5 and 6 in the range. |
A function is commonly denoted by f. In function notation, the symbol f (x), is read "f of x " or "a function of x." Note that f (x) does not mean "f times x." The expression y = f (x) indicates that for every value that replaces x, the function assigns only one replacement value for y.
Let's look at the procedure when using function notation. For example, when the value of x is 4, in the example below, f (4), read "f of 4," represents the value of the function at x = 4.
Example 2:
f (x) = 3x + 5
Let x = 4, then f (4) =3(4) + 5
So, f (4) = 17
This indicates that the ordered pair (4, 17) is a solution of the function.
The vertical line test can be applied to the graph of a relation. If every vertical line drawn on the graph of a relation passes through no more than one point of the graph, then the relation is a function.
A discrete function is a function whose graph consists of points that are not connected.
A continuous function can be graphed with a line or a smooth curve and has a domain with an infinite number of elements.
Continuous
Discrete
