Module C Outcome 7 Polynomial Key Features

Given the polynomial $p\left(x\right)=3x^3-4x^2-3x+4$ check all that applies. 

• The x-intercepts are x = -1, x = 1 and x = 1.33

• The x-intercepts are x = -1, x = 1 and x=2

• The function is a cubic which means it is degree 3

• The function is a quartic which means it is degree 4

• The y-intercept is 4

Given the polynomial $p\left(x\right)=3x^3-4x^2-3x+4$ check all that applies.

• The function is decreasing on the intervalsundefined

Given the polynomial $g\left(x\right)=\ x^4-13x^2$ , Check all of the true statements

• g(x) is a quartic and is degree 4

• g(x) is a cubic and is degree 4

• g(x) has 3 real roots x = -3.606, x= 0 and x= 3.606. AND x= 0 has a multiplicity of 2 which means the root counts twice since it touches the x-axis but does not cross the x-axis.

• g(x) has 3 real roots x = -3.606, x= 0 and x= 3.606. and one imaginary complex root which is why the 4th is not showing.

Given the polynomial $g\left(x\right)=\ x^4-13x^2$ , Check all of the true statements

• The Polynomial has two local minimums at (-2.55, -42.25) and (2.55, -42.25)

• The polynomial has a maximum at $\infty$

• $as\ x\rightarrow\infty,\ g\left(x\right)\rightarrow-\infty$
  

• g(3)=-36

• The polynomial $h\left(x\right)=\ x^2\left(x+3.606\right)\left(x-3.606\right)$ is equivalent (or the same) as g(x)

• The companies value decreased on the interval of (.845, 3.155)

• The companies value at year 6 was 48 million dollars

• The Binomial (x-4) is a factor if k = 1

• The binomial (x+2) is a factor if k = -8

• The binomial (x-20) is a factor is k=-19

• The binomial (x-1) is a factor if k=-19

Many businesses know that most consumers associate price with quality. An actuary at a cosmetics manufacturer determined that the profit made the price charged for lipstick at a particular retail outlet could by modeled by:

 $v\left(p\right)=-0.5p^3+12p^2-17p$  

where p is the price in dollars and v(p) is the amount earned by the retail store selling just the lipstick in a month. 

• When the price of lipstick is $15.26 the cosmetics manufacturer maximizes at $758.21

• The cosmetics manufacturer loses money until they charge $1.51 and if they charge more than $22.49

• The company can intend to make money on the price interval (1.51,22.49)

• The factored form  $g\left(x\right)=-.5x\left(x-1.512\right)\left(x-22.488\right)$  

Given $p\left(x\right)\ =\ 200\left(.75\right)^{\left(2x-3\right)}$  , Check all that apply

•  $p^{-1}\left(x\right)=\frac{1}{2}\log_{.75}\left(\frac{x}{200}\right)\ +\frac{3}{2}$  

•  $p^{-1}\left(x\right)=\frac{\log_{.75}\left(\frac{x}{200}\right)-3}{2}$  

• p(4)= 50

•  $p^{-1}\left(4.75\right)=8$  

• The transformations that occur are as follows: translates right 5 and down 7. vertical stretch of 2

• The transformations that occur are as follows: translates left 5 and down 7. vertical stretch of 2

Which of the following polynomials models the graph given?

• $p\left(x\right)=\ .15\left(x-1\right)^2\left(x+3\right)\left(x-4\right)^3$

• $p\left(x\right)=.15\left(x+1\right)^2\left(x-3\right)\left(x+4\right)^3$

• $p\left(x\right)=-2.4\left(x+3\right)\left(x-1\right)\left(x-4\right)^{ }$

• $p\left(x\right)=-2.4\left(x-3\right)\left(x+1\right)\left(x+4\right)$