A2_4.2 Video Lesson - Zeros and Multiplicity

What does a 'zero of a function' represent on a graph?

• Where the graph crosses the y-axis

• The highest or lowest point of the graph

• Where the graph crosses the x-axis

• The slope of the graph

Tags

CCSS.HSF-IF.C.7C

If 'c' is a solution to a polynomial function, which of the following is a factor of that polynomial?

• (x + c)

• (x - c)

• (c - x)

• (x * c)

Tags

CCSS.HSA.APR.B.2

What happens to the graph of a polynomial function at an x-intercept if its corresponding factor has an odd multiplicity?

• The graph bounces off the x-axis

• The graph goes through the x-axis

• The graph approaches infinity

• The graph has a horizontal asymptote

How does the graph of a polynomial function behave at an x-intercept if its corresponding factor has an even multiplicity?

• The graph goes through the x-axis

• The graph bounces off the x-axis

• The graph becomes a straight line

• The graph has a vertical asymptote

Groups:

(a) first factor

,

(b) second factor

,

(c) third factor

,

(d) extras (not used)

• bounce(2)

• root = 3

• mult = 2

• mult = 3

• through(2)

• root = 4

• mult = 4

• root = 2

• root = 1

• root = -5

• through(1)

• mult = 1

• f(x)

• root = 0

• bounce(1)

• 0 and 3

• 0 and -3

• 1 and 3

• 1 and -3

Tags

CCSS.HSF-IF.C.7C

• x = 0 has multiplicity 1,

  x = 3 has multiplicity 2

• x = 0 has multiplicity 2,

  x = 3 has multiplicity 1

• x = 0 has multiplicity 1,

  x = 3 has multiplicity 1

• x = 0 has multiplicity 3,

  x = 3 has multiplicity 2

Tags

CCSS.HSF-IF.C.7C

• It goes through

  the x-axis.

• It bounces off

  the x-axis.

• It approaches an asymptote.

• It is undefined.

Organize the steps to complete CYU #2 into the right order.

• determine roots, multiplicity, and graph trait

• Factor completely

• plot zeros

• set each factor equal to zero

• use leading term and multiplicity to sketch graph of function