1.If f (x)= square root x^2 -1 and g (x) = square root x-1 , which expression represents f (x)/g(x) for x >1 ?
A. square root x-1
B. square root x
C. 1 square root x+1
D.square root x+1
My answer was D.
2. f (x)=x^2 +3 upward 10 units
A. g (x)= (x +13 )^2
B. g (x)= ( x +10)^2+3
C. g (x)= x^2-7
D. g (x)= x^2+13
My answer was B.
3. f (x) =(x+14)^2 to the right 5 units
A. g (x)= (x-1)^2
B. g (x)=(x+9)^2
C. g (x)= (x+4)^2-5
D. g (x)=(x+4)^2+5
My answer was C.
looking at the possible answers, you must have meant:
f(x) = √(x^2-1) and g(x) = √(x-1)
notice how important the brackets are ???
so f(x) / g(x)
= √(x^2 - 1)/√(x-1)
= √[ (x+1)(x-1)/(x-1) ]
= √(x+1) , x ≠ 1
2. f(x) = x^2 + 3 moved up 10 units is
f(x) = x^2 + 13
3. f(x) = (x+14)^2 to the right 5 units is
f(x) = (x+9)^2
remember moving up or down becomes addition or subtraction of the constant at the end
moving right or left becomes subtraction or addition within the bracket
e.g f(x) = x^2 vs f(x) = (x-4)^2 ---> horizontal shif to the right of 4
f(x) = x^2 vs f(x) = x^2 - 6 ---> vertically down 6 units