Characteristics of Graphs

Is the leading coefficient for the polynomial shown positive or negative?

• Negative

• Positive

• Cannot be determined

Which one of the following could be the polynomial seen in the image?

• y = (x + 3)(x + 1)(x − 2)

• y = -(x + 3)(x + 1)(x − 2)

• y = -(x − 3)(x + 1)(x + 2)

• y = (x + 3)(x + 1)(x + 2)

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)
• f(x) = (x-4)(x+1)²(x+2)(x+4)
• f(x) = (x-4)(x-1)²(x-2)(x+4)
• f(x) = (x+4)(x+1)²(x-2)(x-4)

Which root has a multiplicity of 2?

• -1

• 2

• 4

• -4

The polynomial is...

• Odd degree, positive leading coefficient.
• Odd degree, negative leading coefficient.
• Even degree, positive leading coefficient.
• Even degree, negative leading coefficient.

• (-∞, ∞)
• [-2, 2]
• (-2, 2)
• [-5, 5]

What is the range of the graph?

• -15 < y < ∞
• (-∞, ∞)
• (-15, ∞)
• [-15, ∞)

What is the relative max?

• (0, 36)
• (-2.55, -6.55), (2.55, -6.55)
• (-∞, ∞)
• None

What is the relative min?

• (0, 36)
• (-2.55, -6.55), (2.55, -6.55)
• (-∞, ∞)
• None

What is the end behavior as x → -∞ f(x)→ ?

• -∞
• ∞