2.3 Polynomials and Their Graphs

​ 2.3 Polynomial Functions and Their Graphs

Home

Open in new tab

Copy link

Multiple Choice

The function shown has: #1

• Degree two with negative leading coefficient.

• Degree three with negative leading coefficient.

• Degree four with negative leading coefficient.

• Degree four with positive leading coefficient.

Multiple Choice

What is the end behavior of the function?

y = x⁶ - 7x⁵ + 7x - 9

• as x-> -∞  f(x) -> ∞
   as x-> ∞  f(x) -> -∞
• as x-> -∞ f(x) -> ∞
   as x-> ∞  f(x) -> ∞
• as x->-∞ f(x) -> -∞
   as x-> ∞   f(x) -> ∞
• as x-> -∞ f(x) -> -∞
   as x-> ∞ f(x) -> -∞

Multiple Choice

In the above graph complete the following end behavior: #7

As x --> -∞, f(x) --> ____ As x --> +∞, f(x) --> ____

• -∞
  -∞
• +∞
  -∞
• -∞
  +∞
• +∞
  +∞

Multiple Choice

 Find the correct end behavior diagram for the given polynomial function. $$f\left(x\right)=-x^5-3x^3-2x+8$$  #19

Multiple Select

Select all the graphs which show even degree functions. #2

Home

Open in new tab

Copy link

Multiple Choice

#5

• y =  ^_(x + 2)(x - 1)²
• y = -(x - 2)(x + 1)²
• y = (x - 2)(x + 1)²
• y = -x³

Multiple Choice

#6

• y = x(x - 3)(x - 2)
• y = x(x - 3)² (x+2)
• y = x(x + 3)² (x - 2)
• y = -x(x + 3)² (x - 2)

Multiple Choice

What are the zeros of the function? #9

• 4,1
• 3,1,-2,-5
• -3, -1, 2, 5
• -2,4

Multiple Choice

From the functions below, find the QUARTIC Function. #13

• $$f\left(x\right)=3x-9x^3-7x^4$$

• $$f\left(x\right)=3x^2-11x+9$$

• $$f\left(x\right)=2x-9x^3+11x^2-9x^5-10$$

• $$f\left(x\right)=x^3-8x^2-10x+9$$

To solve a polynomial means to do all these things:

• find the solutions

• find the zeroes

• find the roots

• find the x-intercepts

Synthetic Division

• If dividing by x - 5, the value 5 would go into the top-left box

• The number in the bottom right box is the remainder

• If the remainder is zero, then the # in the top left box is a zero

• f(-2), the y-value when x=-2, is equal to the remainder of the synthetic division with -2 in the top-left box

Home

Open in new tab

Copy link

Multiple Choice

Is x - 3 a factor of the polynomial shown in this synthetic division problem? (NOT ON THE PACKET)

• Yes

• No

Multiple Choice

Find all zeros for the polynomial function P(x) = x³ -3x²-5x+15. #23

• 3, √5 
• 3, √5, -√5
• -3, √5, -√5
• -3, 5i, -5i

Multiple Choice

Determine the roots of the polynomial.  f(x) = -x(x+1)(x-3) #12

• -1, 3
• 0, -1, 3
• 1, -3
• 0, -3, 1

Multiple Choice

Use substitution to determine if -1 is a zero of the given polynomial function. $$f\left(x\right)=8x^3+x^2-7x+6$$  #21

• yes

• no

Multiple Choice

What are the zeros of the function $$g\left(x\right)=\left(x+6\right)\left(x-4\right)\left(x+2\right)$$  ? #25

• $$-6,\ -4,\ -2$$  

• $$-4,\ 2,\ 6$$  

• $$-6\ -2,\ 4$$  

• $$2,\ 4,\ 6$$  

Multiple Choice

Factor:  x³-12x²+47x-60=0 when 5 is a root. #26

• (x-3)(x-4)(x-5)=0
• (x+1)(x-4)(x-5)=0
• (x-3)(x-4)(2x-5)=0
• (x-5)(x-4)(x-5)=0

Multiple Choice

Given that  $$x=1$$   zero of the function $$f\left(x\right)=x^3-9x^2+2x+6$$    use synthetic division to help you find all of the other zeros. All solutions must be exact - no approximate answers. #27

• $$x=4\pm i\sqrt{10}$$  

• $$x=4\pm i\sqrt{22}$$  

• $$x=4\pm\sqrt{22}$$  

• $$x=-4\pm\sqrt{22}$$  

Multiple Select

Given  $$x=-3$$  is a zero of the polynomial  $$f\left(x\right)\ =\ x^3-13x-12$$  , use synthetic division to find all of the other zeros.  Choose ALL that apply. #37

• $$x=1$$  

• $$x=4$$  

• $$x=-1$$  

• $$x=-4$$  

• $$x=3$$  

Multiple Choice

Which one could be a representation of the equation of this graph? #32

• $$-x\left(x-4\right)\left(x+3\right)\left(x+7\right)$$  

• $$-x\left(x+4\right)\left(x-3\right)\left(x-7\right)$$  

• $$x\left(x-4\right)\left(x+3\right)\left(x+7\right)$$  

• $$x\left(x+4\right)\left(x-3\right)\left(x-7\right)$$