Is x=y^2 a One to One Function?

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In summary, the conversation discusses the one-to-one properties of two functions: y=x^2 and x=y^2. The first function is not one-to-one, while the second function's one-to-one status depends on the roles of x and y as independent and dependent variables. The conversation also touches on the use of the vertical line test to determine if a graph is a function. The conversation ends with the question being closed as it has already been answered.
  • #1
Hepic
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I want to make one question. I know that function with that equation: y=x^2 is not one to one.
What about x=y^2 ??

It is one to one or nope??(I know what means one by one,but I am a bit confused,answering in my question,everything will be clear.)
Thanks!
 
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  • #2
Are you asking about x as a function of y, or is y intended to still be a function of x? If x is a function of y, then it is still the case that if I plug in y or -y, I get the same value of x, so it's not one to one. If y is supposed to be a function of x then you haven't actually defined a function, as given an x value there are multiple y values that could work.
 
  • #3
I just ask if this function:y=x^2 is one to one.
 
  • #4
Hepic said:
I just ask if this function:y=x^2 is one to one.

In your original entry you said you know it is not. What is your question? Simply moving letters around does not make it any clearer.
 
  • #5
Sorry,that was my wrong.
By the way both functions(y=x^2 and x=y^2) are one to one,or no?
 
  • #6
You had it right in your first post -- y = x2 is NOT a one-to-one function.

For x = y2, the answer depends on whether x is the dependent variable or y is.

If x is the dependent variable (i.e., x is a function of y), then the graph of x = y2 looks just like the graph of y = 2, but the first graph has the axes labeled differently.

If x is the independent variable, then the equation x = y2 can be rewritten as y = ±√x. Since there are two y values for most x values in the domain, this isn't even a function, let alone a one-to-one function.
 
  • #8
You have already been told, it is NOT a function.
 
  • #9
Hepic said:
http://www.mathwarehouse.com/geometry/parabola/images/x=y2_vertical_line_test.gif

This function is one by one?
The image you posted could be clearer if the two axes were labeled. From the graph and the equation, the vertical axis has to be the y-axis, and the horizontal axis has to be the x-axis.

The image shows a vertical red line, so wherever you got this was probably showing an example of using the vertical line test. What does your book (or wherever you got this image) say about a graph for which a vertical line intersects two or more points?
 
  • #10
The question has been asked and answered, so I'm closing this thread.
 

1. What is a one-to-one function?

A one-to-one function is a type of mathematical function where each unique input value corresponds to one unique output value. This means that for every x value, there is only one y value. In other words, the function passes the horizontal line test, meaning that no horizontal line intersects the function more than once.

2. How can you determine if a function is one-to-one?

To determine if a function is one-to-one, you can graph the function and check if any horizontal lines intersect the function more than once. Another way is to use the horizontal line test, where you draw a horizontal line across the function and if it intersects the function more than once, then the function is not one-to-one.

3. Is the function x=y^2 a one-to-one function?

No, the function x=y^2 is not a one-to-one function. When graphed, it forms a parabola which does not pass the horizontal line test. This means that there are multiple y values for certain x values, making it not a one-to-one function.

4. Can a function be one-to-one if it has the same input and output values?

Yes, a function can be one-to-one even if it has the same input and output values. This is known as a constant function where every x value corresponds to the same y value. While it may not seem like a one-to-one function, it still follows the rule that each unique input value has only one unique output value.

5. Can a function be one-to-one if it has the same output values for different input values?

No, a function cannot be one-to-one if it has the same output values for different input values. This would violate the rule that each unique input value must correspond to one unique output value. In a one-to-one function, each input value must have its own unique output value, even if multiple input values have the same output value.

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