Question

a study was done on snail’s oxygen consumption as a function of ph, and the result was a degree 4 polynomial function whose graph is shown below. which statement about this function is incorrect? a the degree of the polynomial is even. b there is a positive leading coefficient. c at two ph values, there is a relative maximum value. d there are two intervals where the function is decreasing.

Explanation:

• Option A: The polynomial is degree 4, which is even. Correct.
• Option B: For a degree 4 polynomial, as \( x \to \pm\infty \), if the leading coefficient is positive, the graph should go to \( +\infty \). But here, as \( x \) moves away from the middle (towards very low or very high pH, though the domain is limited), the function approaches 0. So the leading coefficient should be negative. Thus, this statement is incorrect.
• Option C: The graph has two peaks (relative maxima), so at two pH values, there's a relative maximum. Correct.
• Option D: Looking at the graph, there are two intervals where the function decreases (from first peak to the valley, and from second peak to pH = 10). Correct.

Answer:

B. There is a positive leading coefficient.