What Kind of Equation is This? f(x)=sqrt(1-(x-1)^2), g(x)=sqrt(1-(x-3)^2), h(x)=sqrt(

[SushiSalad]

I have the functions

f(x)=sqrt(1-(x-1)^2)

g(x)=sqrt(1-(x-3)^2)

h(x)=sqrt(1-(x-5)^2)

When I add them together to make

f(x)+g(x)+h(x)

and I try to graph it, nothing comes up.
Is this some kind of special ungraphable equation?

 

[crybloodwing]

I have the functions

f(x)=sqrt(1-(x-1)^2)

g(x)=sqrt(1-(x-3)^2)

h(x)=sqrt(1-(x-5)^2)

When I add them together to make

f(x)+g(x)+h(x)

and I try to graph it, nothing comes up.
Is this some kind of special ungraphable equation?

The max f(x) g(x) and h(x) can be is 1 because the square root of a negative number is imaginary and won't show on a graph. So you can't subtract anything higher than 1 from 1, and because(x-1) (x-3) and (x-5) are squared, you can never have a negative number that you subtract from 1, therefore adding it.

The lowest it can be is 0 if you have 1-1 under the square root. Then you have to solve for when this is possible. You want what is under the sqrt to be between 0 and 1. So solve for X with these numbers and you get

The max value of X for equation 1 is 2. The min value is 0.

The max value of X for equation 2 is 4. The min value is 2.

The max value of X for equation 3 is 6. The min value is 4.


Equation 1. X is between 0 and 2
Equation 2. X is between 2 and 4
Equation 3. X is between 4 and 6

None of these numbers fit all 3 equations, so one equation will always be undefined. Therefore, it is undefined for all X-Values.

 

[Dr.Peterson]

I have the functions

f(x)=sqrt(1-(x-1)^2)

g(x)=sqrt(1-(x-3)^2)

h(x)=sqrt(1-(x-5)^2)

When I add them together to make

f(x)+g(x)+h(x)

and I try to graph it, nothing comes up.
Is this some kind of special ungraphable equation?

Did you try graphing them individually?

You will see that the graphs are semicircles with radius 1, centered at 1, 3, and 5 on the x-axis, respectively. There are no values of x for which all three are defined. (If you graphed the sum of only f+g or only g+h, the graph would consist of one point. Do you see why?)

 

[Steven G]

I have the functions

f(x)=sqrt(1-(x-1)^2)

g(x)=sqrt(1-(x-3)^2)

h(x)=sqrt(1-(x-5)^2)

When I add them together to make

f(x)+g(x)+h(x)

and I try to graph it, nothing comes up.
Is this some kind of special ungraphable equation?

Hmm, is it ungraphable? Let j(x) = f(x)+g(x)+h(x). Can you compute j(1/2) for example? If you can, then it is graphable as it has at least one point (if by ungraphable you mean there are no points)