I'd start by writing an equation for each of the right triangles. (Pythagorean theorem)
y² + 9² = z²
x² + z² = (4+9)²
4² + y² = x²
we want to find z so combine the equations by substituting the other variables x,y out.
substitute y² for (x² - 4²) in 1st equation.
(x² - 4²) + 9² = z²
now by rearranging the 2nd equation we can substitute x² for (13² - z²)
(13² - z²) - 4² + 9² = z²
169 - z² - 16 + 81 = z²
234 - z² = z²
234 = 2z²
234/2 = z²
117 = z²
√(117) = z
√(9*13) = z
3√(13) = z
13 goes in the box
For x > 2, you would circle the 2, but you would not shade it in because it is greater than/ less than, not greater than or equal to/less than or equal to. From there on, you would move it to the right, because here x is greater than 2, and the numbers to the right of 2 are greater than two.
For x < 2, you would again circle the 2, but don't shade it in. And then you would make a line heading towards the left, because the numbers to the left of 2 are smaller than 2, and here, x is smaller than 2, since 2 is greater.
A value that is not the solution to either inequality is 2. 2 is not greater than 2, and 2 is not less than 2.
So basically right down the graph coordinates for each one for example H is (-4,-1) and just write the opposite for it so H' is (4,1) does that makes sense?
