Table of Contents
- 1 Can a function have the same X and Y-values?
- 2 Can ordered pairs have the same x-value?
- 3 What is the set of Y values?
- 4 How do you know if a graph represents a function?
- 5 What is the difference between function and one-to-one function?
- 6 What is not a function?
- 7 How is a function different from a relation?
- 8 Can a function have an X input with two Y outputs?
Can a function have the same X and Y-values?
To put it concisely: In a function, there can only be one x-value for each y-value. There can be duplicate y-values but not duplicate x-values in a function.
Can ordered pairs have the same x-value?
Functions and Relations A relation is just a set of ordered pairs (x,y) . This just says that in a function, you can’t have two ordered pairs with the same x -value but different y -values. If you have the graph of a relation, you can use the vertical line test to find out whether the relation is a function.
Can a one to one function have the same x-value?
Solution: For a function to be a one to one function, each element from D must pair up with a unique element from C. In the first option, the same value of x is mapped with each value of y, so it cannot be considered as a function and, hence it is not a one-to-one function.
How do you know if a function is not a function?
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
What is the set of Y values?
The Set Of x Values Of A Function, This Is Another Name For Domain . The Set Of y values Of a Function, This Is Another Name For Range . This Is The Horizontal Axis In A Coordinate Graph . This Is The Vertical Axis In a Coordinate Graph .
How do you know if a graph represents a function?
Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.
Can X have more than one Y value?
As long as an x-value doesn’t give multiple y-values, the equation will be a function. Example 1 The equation y=−2x+4 only gives one y-value for any x-value. Therefore, it is a function.
How do you know if a function is one-to-one without graphing?
Use the Horizontal Line Test. If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 . A function f has an inverse f−1 (read f inverse) if and only if the function is 1 -to- 1 .
What is the difference between function and one-to-one function?
A graph of a function can also be used to determine whether a function is one-to-one using the horizontal line test: If each horizontal line crosses the graph of a function at no more than one point, then the function is one-to-one.
What is not a function?
If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.
Is the relation between Y and X a function?
This relation is definitely a function because every x-value is unique and is associated with only one value of y. So for a quick summary, if you see any duplicates or repetitions in the x-values, the relation is not a function.
Can you make X and Y have the same value?
How you define these will affect how you work out the problem, but does not affect the solution. One reader was concerned by the fact that you can end up with two variables having the same value: a half-coconut has the same value as a banana, and “this is not algebraically correct, as in algebra, X & Y cannot both be equal to one.”
How is a function different from a relation?
A function is a special type of relation . A relation is just a set of ordered pairs ( x, y) . In formal mathematical language, a function is a relation for which: if ( x 1, y) and ( x 2, y) are both in the relation, then x 1 = x 2 . This just says that in a function, you can’t have two ordered pairs with the same x -value but different y -values.
Can a function have an X input with two Y outputs?
Can a function have an x input with two y outputs? Please forgive me if my example is atrocious, hopefully it gets my point across. This seems like a good time to learn about what it means for an expression to be well-defined. No doubt you are comfortable with integer arithmetic; we may define addition of fractions by (1) x y + p q = x q + p y y q.