Question

40 POINTS!!!!

graph the function g(x) = x3 − x2 − 4x + 4. (an actual graph that you can attach)

Answer 1

see below

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