Answer:
Step-by-step explanation:
f(x) = x⁵ – 8x⁴ + 16x³
As x approaches +∞, the highest term, x⁵, approaches +∞.
As x approaches -∞, x⁵ approaches -∞ (a negative number raised to an odd exponent is also negative).
Now let's factor:
f(x) = x³ (x² – 8x + 16)
f(x) = x³ (x – 4)²
f(x) has roots at x=0 and x=4. x=4 is a repeated root (because it's squared), so the graph touches the x-axis but does not cross at x=4.
The graph crosses the x-axis at x=0.
