Question

the graph to the right is a complete graph, that is, it is continuous and displays the functions end behavior. all zeros are integers. answer the following questions.

(a) list the zeros whose multiplicity is even. select the correct choice below and fill in any answer boxes within your choice.
a. (type an integers or a simplified fractions. use a comma to separate answers as needed.)
b. there are no such zeros.

list the zeros whose multiplicity is odd. select the correct choice below and fill in any answer boxes within your choice.
a. (type an integers or a simplified fractions. use a comma to separate answers as needed.)
b. there are no such zeros.

Explanation:

Identify graph behavior at each x-intercept

Using the Graph Behavior at Zeros knowledge point

• The graph crosses the x-axis at \(x = -1\).
• The graph touches the x-axis and turns around at \(x = 0\).
• The graph crosses the x-axis at \(x = 2\).

Determine zeros with even multiplicity

Using the Multiplicity of Zeros knowledge point

• Even multiplicity causes the graph to touch the x-axis and turn around.
• This behavior occurs at \(x = 0\).
• Therefore, the zero with even multiplicity is \(0\).

Determine zeros with odd multiplicity

Using the Multiplicity of Zeros knowledge point

• Odd multiplicity causes the graph to cross the x-axis.
• This behavior occurs at \(x = -1\) and \(x = 2\).
• Therefore, the zeros with odd multiplicity are \(-1, 2\).

Answer:

Question 1

• A. 0 (Type an integers or a simplified fractions. Use a comma to separate answers as needed.) (Correct answer)
• B. There are no such zeros.

Question 2

• A. -1, 2 (Type an integers or a simplified fractions. Use a comma to separate answers as needed.) (Correct answer)
• B. There are no such zeros.