Answer:
see below
Step-by-step explanation:
g(x) = x^3 − x^2 − 4x + 4
We know the graph will have up to 3 zero's because it is a cubic
g(x) = x^3 − x^2 − 4^x + 4
I will factor by grouping, taking an x^2 from the first 2 terms and -4 from the last 2 terms
g(x)= x^2(x-1) -4(x-1)
Now factor out x-1
g(x)= (x-1)(x^2 -4)
We can factor the (x^2-4) as a difference of squares
g(x) = (x-1) (x-2)(x+2)
Using the zero product property
0= (x-1) (x-2)(x+2)
x-1 =0 x-2 =0 x+2=0
We have zeros at x=1 x=2 and x=-2
Then we can plot points to determine where the function is between the points We will pick negative infinity 0 1.5 and infinity
at g(-inf) = -inf because x^3 dominates and that goes to -infinity
at g(0) = 0+000+4 =4
at g(1.5) =-.875
at g(inf)=because x^3 dominates and that goes to infinity
