Understanding Repeated Zeros in Polynomial Functions

What is the maximum number of distinct complex zeros a polynomial of degree n can have?

• n-1

• 2n

• n

• n+1

When graphing the function x - 3 * (x + 2)^2, what happens at x = 3?

• The graph crosses the x-axis

• The graph touches the x-axis

• The graph is undefined

• The graph has a vertical asymptote

In the function x - 3^2 * (x + 2)^3, what is the behavior of the graph at x = -2?

• The graph has a hole

• The graph crosses the x-axis

• The graph is undefined

• The graph touches the x-axis

What determines whether a graph crosses or touches the x-axis at a zero?

• The multiplicity of the zero

• The degree of the polynomial

• The leading coefficient

• The constant term

If a zero has an odd multiplicity, what is the behavior of the graph at that zero?

• The graph has a vertical asymptote

• The graph is undefined

• The graph crosses the x-axis

• The graph touches the x-axis

For a zero with even multiplicity, what does the graph do at that point?

• The graph has a vertical asymptote

• The graph crosses the x-axis

• The graph is undefined

• The graph touches the x-axis

In the function f(x) = (x - 7)^4 * (x + 1)^6 * (x - 8)^7, what is the behavior of the graph at x = 7?

• The graph has a vertical asymptote

• The graph touches the x-axis

• The graph crosses the x-axis

• The graph is undefined

What is the multiplicity of the zero at x = -1 in the function f(x) = (x - 7)^4 * (x + 1)^6 * (x - 8)^7?

• 6

• 4

• 7

• 1

In the function f(x) = (x - 7)^4 * (x + 1)^6 * (x - 8)^7, what is the behavior of the graph at x = 8?

• The graph has a vertical asymptote

• The graph touches the x-axis

• The graph is undefined

• The graph crosses the x-axis

What is the significance of knowing the multiplicity of zeros before graphing a polynomial?

• It helps in predicting the graph's behavior at those zeros

• It helps in determining the degree of the polynomial

• It helps in finding the leading coefficient

• It helps in identifying the constant term