Answer
See graph and explanations.
Work Step by Step
Step 1. Given $f(x)=x^3+x^2-12x$, we have
$f(-x)=-x^3+x^2+12x$
Thus, there is no symmetry.
Step 2. The degree of the power is 3 and the leading coefficient is $+1$. The end behaviors are falling to the left and rising to the right.
Step 3. Find the x-intercepts:
$f(x)=x(x^2+x-12)=x(x+4)(x-3)$
Thus we have
$x=-4,0,3$
Step 4. Find the y-intercept: $f(0)=0$
Step 5. Maximum number of turns $3-1=2$
Step 6. Using test points and the information above, we can graph the function as shown.
