Question: Question 6 - of 7 Step 2 of 2 Consider the following polynomial. \[ h(x) = 8x^2 - 6x - 11 \]…

Question 6 - of 7 Step 2 of 2

Consider the following polynomial.

\[ h(x) = 8x^2 - 6x - 11 \]

Step 2 of 2: Describe the behavior of the graph of \( h(x) \) as \( x \to \pm \infty \).

Answer 4 Points

\[ h(x) \to \boxed{\quad} \text{ as } x \to -\infty \]

\[ h(x) \to \boxed{\quad} \text{ as } x \to \infty \]

Show Work

Solution

Step 1: Identify the leading term of the polynomial. \[ h(x) = 8x^2 - 6x - 11 \] Step 2: Determine the degree and the leading coefficient. - The degree of the polynomial is 2. - The leading coefficient is 8, which is positive. Step 3: Analyze the end behavior based on the leading term. - Since the degree is even and the leading coefficient is positive, as \( x \) approaches both \( -\infty \) and \( +\infty \), \( h(x) \) will approach \( +\infty \). Step 4: Fill in the answer template. \[ \begin{cases} h(x) \rightarrow +\infty & \text{as } x \rightarrow -\infty \\ h(x) \rightarrow +\infty & \text{as } x \rightarrow \infty \\ \end{cases} \]