SOLUTION: Determine whether this relation defines a function (Could you show the work Im struggling with this problem) x-4y=8

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Question 1199064: Determine whether this relation defines a function (Could you show the work Im struggling with this problem)
x-4y=8
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
Determine whether this relation defines a function (Could you show the work Im struggling with this problem)
x-4y=8
~~~~~~~~~~~~~~~~~


For any input value of x this relation defines a unique output value for y

            y = %28x-8%29%2F4.

So,  the given relation/formula does define a function.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Use the graphing tool Desmos to type in exactly what is given.
It will produce a straight line as shown in this link.
https://www.desmos.com/calculator/pp87lovs1g

In case you're not able to visit the link, this is what the screenshot would look like (similar to it)
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-100%2C%288-x%29%2F%28-4%29%29

To see if we have a function or not, we use the vertical line test.
This is where we try to pass a single vertical line through more than one point on the green line above.
As you can probably tell, it is impossible to draw such a vertical line.
Each vertical line goes through *exactly* one and only one point on the green line.
This means each input (x) leads to exactly one output (y).

In short: one input ---> one output

Therefore, this graph passes the vertical line test and we have a function.

---------------------------------------------------

Here's an example of a non-function
x^2+y^2 = 25
This plots out a circle of radius 5, centered at the origin

Now it is fairly clear that we can pass a single vertical line through more than one point on the green curve.
For example, we can pass a vertical line through x = 0 to have it intersect at (0,5) and (0,-5)
This leads to the graph failing the vertical line test and we don't have a function.

Another example of a non-function
x = y^2
This produces a sideways parabola opening to the right
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-100%2Csqrt%28x%29%2C-sqrt%28x%29%29
The upper and lower pieces (sqrt%28x%29 and -sqrt%28x%29 respectively) combine to form the entire curve treated as one single entity.

I recommend you typing these examples into Desmos to interact with the graph. I also recommend exploring other examples of functions and non-functions.

GeoGebra is a similar graphing tool that I use all the time as well. Both graphing tools are free.