Question

29. Identify the end behavior of the function f(x) = 3x^4 + x^3 − 7x^2 + 12.

options:
A. As x → –∞, y → +∞, and as x → +∞, y → –∞

B. As x → –∞, y → –∞, and as x → +∞, y → –∞

C. As x → –∞, y → +∞, and as x → +∞, y → +∞

D. As x → –∞, y → –∞, and as x → +∞, y → +∞

Answer 1

C. As x → –∞, y → +∞, and as x → +∞, y → +∞

Explanation:

The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.

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When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.

When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.