Question

identifying multiplicity of roots graphically
the graph of f(x) is given.
which roots of f(x) have an odd multiplicity? choose two correct answers.
1
-1
3

Explanation:

To determine the multiplicity of roots graphically, we use the rule: if the graph crosses the x - axis at a root, the multiplicity is odd; if it touches and turns around (a local maximum or minimum on the x - axis), the multiplicity is even.

• For the root \(x = - 1\): The graph crosses the x - axis at \(x=-1\), so its multiplicity is odd.
• For the root \(x = 1\): The graph touches the x - axis at \(x = 1\) (it has a local maximum on the x - axis) and then turns around, so its multiplicity is even.
• For the root \(x=3\): The graph crosses the x - axis at \(x = 3\), so its multiplicity is odd.

Answer:

-1, 3