Question

I need help with my algebra II!!

Answer 1

1st:
f(x) = x^2.
f(x +1):  Anywhere we see x we replace it with (x+1)

f(x+1) = (x+1)^2 , Expand
(x+1)^2 = (x+1)(x+1) = x^2 + 2x + 1=  C.

2nd:
Noting general equation, y = mx + c
m = slope,  c = vertical intercept.
From the graph, slope =  (2,0) and (0, -4)
=  (-4 -0) / (0 - 2) = -4/-2 = 2.
Vertical intercept, c = -4.
y = mx + c ,  y = 2x + (-4),    y = 2x - 4 =  D.

3rd:
f(x) = x^2 - x,  f(-4).  we would substitute x = -4.

f(-4) = (-4)^2 - (-4) = 16 + 4 = 20 = D.
Cheers.