Question

the graph of f(x) is given on the right.
which roots of f(x) have an odd multiplicity?
-1
1
3
could be a multiplicity of the root at x = 1.

Explanation:

Identify the behavior of the graph at \(x = 1\)

$$ \text{At } x = 1, \text{ the graph touches the } x\text{-axis and turns around without crossing it.} $$

Determine the multiplicity type

$$ \text{A root where the graph touches and turns around has an even multiplicity.} $$

Select a possible multiplicity value

$$ \text{Since the multiplicity must be even, a possible value is } 2 \text{ (or any positive even integer like } 4, 6, \dots\text{).} $$

Answer:

<blank>2</blank> could be a multiplicity of the root at \(x = 1\).