Question

What is the end behavior of the graph of f(x) = x5 – 8x4 + 16x3?

The graph touches, but does not cross, the x–axis at x =
.

The graph of the function crosses the x–axis at x =
.

Answer 1

The graph touches, but does not cross, the x–axis at x = 4

The graph of the function crosses the x–axis at x = 0

Explanation:

f(x) = x⁵ – 8x⁴ + 16x³

=x³ (x² - 8x + 16)

= x³ (x-4)²

f(x) = 0 x = 0 or x = 4