Question

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

Answer 1

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.

Answer 2

Answer:

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

Step-by-step explanation: