A polynomial function is given. U(x) = −x3 + 3x2. Y→_______ as x→ ∞

Question

3.2 Polynomial functions (a)

Answer 1

For very large values of x, the highest degree term of the polynomial dominates. So, the end behavior of the highest degree term of the polynomial is the same as the end behavior of the polynomial itself. This works for any polynomial function, other than a constant function.

So, since -x³ → -∞ as x → ∞, -x³ + 3x² → -∞ as x → ∞.

Answer 2

You can also plug in a rather large number and see if it's approaching a particular value or getting huge (either in the positive or negative direction). In this case, you could plug in something like 100 and notice that y= -1,000,000 + 30000 = -970,000. This is rather large in the negative direction, so this graph does not show signs of going back towards a finite value. Therefore, y will approach negative infinity as x approaches positive infinity.

Answer 3

Think of the graph:

Notice that as "x" goes out toward infinity, the "y" value is going toward negative infinity. So you could also say that y → -∞ as x → ∞