Question

consider the following polynomial. h(x) = x² - 9x - 7 step 2 of 2: describe the behavior of the graph of h(x) as x → ±∞. answer 4 points h(x) → as x → -∞ h(x) → as x → ∞

Explanation:

Step1: Identify Leading Term

The polynomial \( h(x) = x^2 - 9x - 7 \) has leading term \( x^2 \), with degree 2 (even) and leading coefficient 1 (positive).

Step2: Analyze End Behavior

For polynomials, when the degree is even and leading coefficient is positive:

• As \( x \to -\infty \), \( x^2 \) (since squaring a large negative number gives a large positive number) dominates, so \( h(x) \to \infty \).
• As \( x \to \infty \), \( x^2 \) (squaring a large positive number gives a large positive number) dominates, so \( h(x) \to \infty \).

Answer:

For \( h(x) \to \) \(\boldsymbol{\infty}\) as \( x \to -\infty \)
For \( h(x) \to \) \(\boldsymbol{\infty}\) as \( x \to \infty \)