Select the correct answer from each drop-down menu.

The graph of the equation y = -x4 + x2 − 2
(A. Increases as x approaches negative infinity and decreases as x approaches positive infinity.)
(B. Decreases as x approaches negative infinity and increases as x approaches positive infinity)
(C. Increases as x approaches negative and positive infinity)
(D. Decreases as x approaches negative and positive infinity)

The graph of the equation y = x5 + x2 + 7
(A. Increases as x approaches negative infinity and decreases as x approaches positive infinity.)
(B. Decreases as x approaches negative infinity and increases as x approaches positive infinity)
(C. Increases as x approaches negative and positive infinity)
(D. Decreases as x approaches negative and positive infinity)

The graph of the equation y = x6 + 2x3 + 3
(A. Increases as x approaches negative infinity and decreases as x approaches positive infinity.)
(B. Decreases as x approaches negative infinity and increases as x approaches positive infinity)
(C. Increases as x approaches negative and positive infinity)
(D. Decreases as x approaches negative and positive infinity)

anyways look at the part with the largest power of x. it will have the biggest impact on the overall value, when x approaches positive or negative infinity.

in the first one this is -x⁴

x⁴ is always positive (for positive and negative x). so, -x⁴ is always negative. therefore, it decreases in both cases when x approaches positive or negative infinity.

in the second one this is x⁵.

this goes with the sign of x. it is getting bigger (it increases), when x approaches positive infinity, and it is getting smaller (it decreases), when x approaches negative infinity.

in the third one this is x⁶.

this is always positive (for positive and negative x). therefore, it increases in both cases when x approaches positive or negative infinity.