Question

If `y = x^3-3x + 2`, then draw the graph of the followings (i) `y=|x^3-3x + 2|`

Answer 1

We have `y=f(x)=|x^(2)-3|x+2|`
Let `g(x)=x^(2)-3x+2`
Then `f(x)=|g(|x|)|`
Graph of `y=g(x)=(x-1)(x-2)` is an upward parabola intersecting the x-axis at (1,0) and (2,0)

Now the graph of `y=g(|x|)=x^(2)-3|x|+2` is as follows.

Finally the graph of `y=|g(|x|)` is as follows.