Understanding Polynomials and Their Graphs

What is the term used to describe a root that touches the x-axis but does not cross it?

• Single root

• Double root

• Triple root

• Quadruple root

If a polynomial has a factor of (x + 3)^2, what can be said about its graph at x = -3?

• The graph is undefined at x = -3

• The graph has a vertical asymptote

• The graph bounces off the x-axis

• The graph crosses the x-axis

How does a positive leading coefficient with an odd degree affect the end behavior of a polynomial graph?

• The graph goes up on the left and down on the right

• The graph goes down on the left and up on the right

• The graph goes down on both ends

• The graph goes up on both ends

What is the y-intercept of the polynomial f(x) = (x - 4)(x - 1)(x + 3)?

• 4

• -12

• 12

• 0

In the polynomial f(x) = x(x + 2)^2(x - 3), what is the multiplicity of the root at x = 0?

• 1

• 2

• 3

• 4

What is the smallest possible degree of a polynomial with roots at -2, 0, 4, and 6, where the root at 0 has a multiplicity of 2?

• 6

• 5

• 4

• 3

If a polynomial graph starts and ends in the same direction, what can be inferred about its degree?

• The degree is odd

• The degree is undefined

• The degree is even

• The degree is zero

Which of the following is NOT a synonym for 'roots' in the context of polynomials?

• Intercepts

• Factors

• Solutions

• Zeros

What is the effect of a negative leading coefficient on the end behavior of a polynomial with an even degree?

• The graph goes up on both ends

• The graph goes down on both ends

• The graph goes down on the left and up on the right

• The graph goes up on the left and down on the right

In the polynomial f(x) = (x + 3)^3(x - 1), what is the behavior of the graph at x = 3?

• The graph is undefined at x = 3

• The graph has a vertical asymptote

• The graph bounces off the x-axis

• The graph crosses the x-axis