Hi, it may be too late but I think I can provide some help on this one.
1/ root(2+x) + root(1-x)
Domain - the numbers that you can set x as. You cannot have the square root of a negative number, so the range will be anything that makes (1-x) ≥ 0 and (2+x) ≥ 0
Answer : -2 ≤ x ≤ 1
Range - the range of numbers that you can get out of the equation. This is suppose would depend if you are allowing -ve roots, you should be able to get an answer from this though.
Note : I occasionally get range + domain backwards so it may be worth double checking.
2/ Passes through (3,5), gradient = 3
Hmm. Try this :
(Y-Y1) / (X-X1) = gradient
In this case, Y1 = 5, Y2 = 3, gradient = 3.
3/ ƒ(x) = x² + 3x – 2
a. ƒ(x) + h - This is just x² + 3x – 2 + h
b. ƒ(x + h) - This means just replace x with (x+h) => (x+h)² + 3(x+h) – 2
c. ƒ(2x) - Just replace x with 2x => (2X)² + 3(2X) – 2
d. ƒ(x + h) - ƒ(x - h) - Similar to part b really =>
[ (x+h)² + 3(x+h) – 2 ] - [ (x-h)² + 3(x-h) – 2 ]
Parts c + d can defaintely be simlified but shouldn't be too difficult once you have muliplied out the brackets.