Answer:
As x→ +∞, f(x)→-∞, and as x→ -∞, f(x)→+∞
Step-by-step explanation:
The end behavior of a fuction represents the behavior of this function at the ends of the x-axis.
In other words, the end behavior is the value of f(x) when x goes to -∞ and f(x) when x goes to +∞
Also, if we have a polynomial function, the end behavior of this function is the same as the end behavior of its leading term, in this case -3x⁵
To find the end behavior, lets substitute x:
As x→ +∞
f(x) → -3x⁵ + bx² - cx + 2
f(x) → -3x⁵
f(x) → -3(+∞)⁵
f(x) → -5∞⁵
f(x) → -∞
x→ -∞
f(x) → -3x⁵ + bx² - cx + 2
f(x) → -3x⁵
f(x) → -3(-∞)⁵
f(x) → +3∞⁵
f(x) → +∞
