Question

if a zero is dropdown, then the graph of its function only touches the \\(x\\)-axis at that zero.

if a zero is dropdown, then the graph of its function crosses the \\(x\\)-axis at that zero.

options in dropdown:
of odd multiplicity
of even multiplicity

Explanation:

Analyze the behavior of even multiplicity

$$ \text{Even multiplicity} \implies \text{Graph touches the } x\text{-axis and turns around.} $$

Analyze the behavior of odd multiplicity

$$ \text{Odd multiplicity} \implies \text{Graph crosses the } x\text{-axis.} $$

Answer:

Question 1

If a zero is <blank>of even multiplicity</blank>, then the graph of its function only touches the \(x\)-axis at that zero.

Question 2

If a zero is <blank>of odd multiplicity</blank>, then the graph of its function crosses the \(x\)-axis at that zero.