Which of the graphs below would result if you made the leading term of the following function negative?

We are given function F(x) = x^3 +3x^2.

Leading term is the term that has highest power of a variable.

For the given function we have highest power 3 of x.

Therefore, leading term is x^3. We don't have any sign in front of x^3. Therefore, it's a positive leading term.

And degree of the is highest power, that is 3.

Therefore, degree is an odd number.

According to problem,  we need to make the leading term as a negative number.

So, we need to find a rule for end behaviour of the graph with:

Leading coefficent = Negative.

Degree : Odd.

Please note the rule, when leading coefficent a negative number and degree is odd.

x--> + ∞   f(x) ---> - ∞

x--> - ∞   f(x) ---> + ∞

We can see option D has  f(x) ---> - ∞ for x--> + ∞ and  f(x) ---> + ∞ for x--> - ∞.

that you could either multiple or u could either add them up until u get to the right answer