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Is a function a relation if and only the x-values do not repeat in a given set?
Wiki User
∙ 12y ago
No.
If an x-value is repeated but both values have the same image, you can still have a valid function.
x values not repeating is not sufficient if there is no image.
For example, consider 1/x and the domain as the integers -3, -2, -1, 0, 1, 2, 3.
None of the x values repeats but there is no functional relationship because 1/x is not even defined for x = 0.
Wiki User
∙ 12y ago
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if a given value yields three output values that relationship can be best described a function?
No, it is described as a relation.
What is the inverse of the given relation?
The inverse of the given relation is obtained through expressing it as 1 over that relation.
How do you evaluate a function for a given input value?
Substitute the given value for the argument of the function.
What name is given to the shape of a quadratic function?
A parabola
What is a gradient in maths?
The gradient of a function, in a given direction, is the change in the value of the function per unit change in the given direction. It is, thus, the rate of change of the function, with respect to the direction. It is generally found by calculating the derivative of the function along the required direction. For a straight line, it is simply the slope. That is the "Rise" divided by the "Run".
if a given value yields three output values that relationship can be best described a function?
No, it is described as a relation.
What is the inverse of the given relation?
The inverse of the given relation is obtained through expressing it as 1 over that relation.
When do you say that a given function is velation?
I assume you mean "relation". By definition, all functions are relations; but only some relations are functions.
How do you identify if the given equation is function or not?
A function is an equation (a relation) which has only one y-value for every x-value. If a single x-value has more than one y-value, the equation is no longer called a function.
How do you determine if you are given a set of ordered pairs that represent a function?
A relation is a set of ordered pairs.A function is a relation such that for each element there is one and only one second element.Example:{(1, 2), (4, 3), (6, 1), (5, 2)}This is a function because every ordered pair has a different first element.Example:{(1, 2), (5, 6), (7, 2), (1, 3)}This is a relation but not a function because when the first element is 1, the second element can be either 2 or 3.
Explain the test that allows us to determine whether a graph is that of a function?
The vertical line test: Imagine a very large family of vertical lines. If any of the lines intersect with the graph of the relation under consideration at more than a single point then the relation is not a function. (Because a function assigns just one value in the range to a given point in the domain.)
How can you tell if a relation of a graph has a function?
A relation is any set of ordered pairs (x, y), such as {(2, 5), (4, 9), (-3, 7), (2, 0)} or {(2, 3), (5, -2)}. A function is a special type of relation in which each x-value is assigned a unique y-value. So in the two examples given above, the first relation is NOT a function because the x-value of 2 is assigned two different y-values: 5 and 0. The second example above is a relation, since each x-value given (i.e., 2 and 5) is only assigned to one y-value (i.e., 3 and -2, respectively). Two additional examples: {(0, 5), (1, 3), (1, 8), (4, -2)} is NOT a function, because the x-value of 1 is assigned to two different y-values. {(0, 3), (1, 4), (3, -2), (4, 7), (5, 0)} is a function, because there is no x-value that is assigned to more than one y-value. When graphed in the Cartesian plane, you can determine if a relation is a function or not by the "vertical line test", which says that if there is any place where a vertical line can be drawn that will pass through the graph more than once, then that relation is NOT a function. But if every vertical line that can possibly be drawn only passes through the relation at most once, then that relation is a function.
What is it called if any vertical line crosses the graph of a relation more than once the relation is not a function?
The Vertical Line Test An example might be x=cos(y). At any value of x between -1 a nd +1 (a vertical line on the graph) this is multivalued (and so it is called "multivalued"). The relation is a function, because given y you can calculate x. x is a function of y. The relation between y and x can also be written y=cos-1(x) "y is the angle whose cosine is x". From that point of view you can say " y is not a function of x" because for each x, there is more than one y that satisfyies the equation. To summarize, in this example x is a function of y but y is not a function of x.
How do you find a domain and range of a relation given by a set of order pairs?
Describe how to find the domain and range of a relation given by a set of ordered pairs.
How do you evaluate a function for a given input value?
Substitute the given value for the argument of the function.
What is the largest equivalence relation on a set A?
An equivalence relation on a set is one that is transitive, reflexive and symmetric. Given a set A with n elements, the largest equivalence relation is AXA since it has n2 elements. Given any element a of the set, the smallest equivalence relation is (a,a) which has n elements.
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