Questions: Use the leading-term test to match the function f(x) = x^5 + 1/12 x - 6 with one of the given graphs. Choose the correct graph below. A. B. C. D.

Solution Steps

The given function is \( f(x) = x^5 + \frac{1}{12}x - 6 \). The leading term is \( x^5 \).

For the leading term \( x^5 \):

• As \( x \to \infty \), \( x^5 \to \infty \).
• As \( x \to -\infty \), \( x^5 \to -\infty \).

This indicates that the graph will rise to the right and fall to the left.

Examine the given graphs:

• Graph A: Falls to the left and rises to the right.
• Graph B: Rises to the left and falls to the right.
• Graph C: Falls to the left and rises to the right.
• Graph D: Rises to the left and falls to the right.

Graphs A and C match the end behavior of the function \( f(x) = x^5 + \frac{1}{12}x - 6 \).

Final Answer