Question

question 36
find the correct end behavior diagram for the given polynomial function.
p(x) = 7x^6 - x^5 + 4x^2 - 3
a

b

c

d

Explanation:

Step1: Identify Degree and Leading Coefficient

The polynomial is \( P(x) = 7x^6 - x^5 + 4x^2 - 3 \). The degree (highest power of \( x \)) is 6 (even), and the leading coefficient (coefficient of \( x^6 \)) is 7 (positive).

Step2: Determine End Behavior

For a polynomial, if the degree is even and the leading coefficient is positive, as \( x \to \infty \), \( P(x) \to \infty \), and as \( x \to -\infty \), \( P(x) \to \infty \) (both ends go up). So the end - behavior diagram should have both arrows pointing upwards.

Answer:

D. \( \uparrow \uparrow \)