Question

Consider the polynomial function q(x) = -4.25 + 2x⁴ – 3x² + 12x. What is the end behavior of the graph of q?

a) Increases without bound as x → [infinity] and decreases without bound as x → -[infinity]
b) Increases without bound as x → -[infinity] and decreases without bound as x → [infinity]
c) Approaches a horizontal line as x → [infinity] and as x → -[infinity]
d) Approaches a vertical line as x → [infinity] and as x → -[infinity]

Answer 1

The end behavior of the polynomial function q(x) = -4.25 + 2x⁴ - 3x² + 12x is that it increases without bound as x approaches positive infinity and decreases without bound as x approaches negative infinity.

Step-by-step explanation:

The end behavior of a polynomial function is determined by the degree and leading coefficient of the function. In this case, the polynomial function q(x) = -4.25 + 2x⁴ - 3x² + 12x has a degree of 4, which is even. The leading coefficient is 2. When the degree is even and the leading coefficient is positive, the end behavior of the graph is as follows:

• As x approaches positive infinity, the graph of q(x) increases without bound.
• As x approaches negative infinity, the graph of q(x) also increases without bound.

Therefore, the correct answer is option a) Increases without bound as x → [infinity] and decreases without bound as x → -[infinity].