Algebra 2 questions help

a few questions i cant figure out in homework.

1. if f(x) = x^3 + 2x^2 -3x -1 , find g(x) = f(x+1).

2.if f(x) = x^4 - x^3 - x^2 - 2x - 3, find g(x), the reflection of f(x) across the y-axis.

3.a quintic polynomial has, at most, how many x-intercepts?
A.3
B.4
C.5
D.6

4. if f(x) = x^2 -2x + 3, which of the following is equal to g(x) = f(x+1)?
A. x^2+2
B. x^2 -2x + 4

1)

f(x) = x^3 + 2x^2 - 3x - 1

f(x + 1)
= (x +1)^3 + 2(x + 1)^2 - 3(x + 1) - 1
= x^3 + 3x^2 + 3x + 1 + 2x^2 + 4x + 2 - 3x - 3 - 1
= x^3 + 5x^2 + 4x - 1

2)

f(x) = x^4 - x^3 - x^2 - 2x - 3

g(x)
= (-x)^4 - (-x)^3 - (-x)^2 - 2(-x) - 3
= x^4 + x^3 - x^2 + 2x - 3

3)

C. 5 x-intercepts.

4)

g(x)
= f(x + 1)
= (x + 1)^2 - 2(x + 1) + 3
= x^2 + 2x + 1 - 2x - 2 + 3
= x^2 + 2