+130516 To find the y intercept, let x = 0 ....and we have.....
f(x)=sqrt(0+4)+sqrt(4-0) = sqrt(4) + sqrt(4) = 2 + 2 = 4 = (0,4)
To find the x intercepts, let y = 0
0 = sqrt (x + 4) + sqrt(4 -x) .... ( 1) subtract sqrt (4 - x) from both sides
-sqrt(4 - x) = sqrt (x + 4) .... (2) square both sides
4 - x = x + 4 add x to both sides......subtract 4 from both sides
0 = 2x divide both sides by 2
0 = x
However.....note that x = 0 makes (1) untrue......it's an extraneous solution produced by squaring both sides of (2)......there aren't any x intercepts - as shown by the following graph :
https://www.desmos.com/calculator/dm9rxpqizk
