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Describe the end behavior for the graph of f(x) = -3x^5 + bx^2 - cx + 2 where b and c are constants.

User Ayub
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1 Answer

28 votes
28 votes

Answer:

As x→ +∞, f(x)→-∞, and as x→ -∞, f(x)→+∞

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) → +∞

User Lucas Willems
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3.0k points
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