Question

If you were given the equation f(x)=3x5−6x, what behavior would the ends of the graph have?

A) The ends approach positive infinity.
B) The ends approach negative infinity.
C) The ends oscillate between positive and negative infinity.
D) The ends approach zero.

Answer 1

The ends of the graph approach positive infinity as x approaches positive infinity and approach negative infinity as x approaches negative infinity.

Step-by-step explanation:

The behavior of the ends of the graph can be determined by analyzing the exponents of the polynomial function.

For the given equation f(x) = 3x5 - 6x:

• As x approaches negative infinity, the term 3x5 becomes more negative while the term -6x remains negative. Therefore, the ends of the graph approach negative infinity, option B.
• As x approaches positive infinity, the term 3x5 becomes more positive while the term -6x remains negative. Therefore, the ends of the graph approach positive infinity, option A.

So, the correct behavior of the ends of the graph is option A and option B.