Karteikarten
MTH107-3
Karten in diesem Stapel (42)
- 1Polynomial Function Standard Form
- 2Leading Term6x^8
- 3Leading Coefficient6
- 4Power functionPolynomial with one term
- 5X^2 vs X^4 vs X^6Less than x=1
X^2 is larger
More than x=1
x^4 is larger
- 6X^3 vs X^5 vs X^7Less than x=1
X^3 is larger
More than x=1
x^5 is larger - 7Rules of flipping graphs of functions"-" leading coefficient = flipped vertically
"+" leading coefficient = normal - 8rules of flipping even and odd degrees
- 9what is the 8?y intercept
also the constant
- 103 root behaviors
- 11If a root appears an EVEN # of times (x-1)^2(x+2)(X+1)X= 1,1,-2,-1
Then x= 1 is a bouncing point - 12If a root appears an ODD # of times (x-1)^2(x+2)(X+1)X= 1,1,-2,-1
Then x= -2,-1 is a through (crossing) point - 13Multiplicity1) For x^2: M=2 (Bounces)
2) For (x-1)^3: M=3 (Crosses)
3)For (x+2)^4: M=4(Bounces)
- 14Multiplicity of x^2gonna be x=0 or (0,0)
- 15What is a root?X Intercept
- 16Rational root theorem what is P? What is q? How are they configured?"P" is divisor of constant terms = 27
"q" is divisor of leading coefficient = 9
configured as "P/q"
- 17What are the factors? P/q ?
- 18What do you do with p/q after that?Divide P's by all Q's
for possible roots,
DONT REPEAT
OUTCOMES
- 19If possible root is plugged into the function and = 0make the function = 0 to find x
If the possible root = 0 then it is a factor
f(1) = 0
X = 1 is a root
(x-1) is a factor
- 20Factoring polynomials Step 1Find "p" and "q"
P = 6
factors of p = +-1,+-2,+-3,+-6
q = 2
factors of q = +-1, +-2
- 21Factoring polynomials Step 2Divide all p's by all q's for possible roots
(dont repeat outcomes if the exist)
possible roots:
+-1, +-1/2, +-2, +-3, +-3/2, +-6 - 22Factoring polynomials Step 3make the function = 0 to find x
If the possible root = 0 then it is a factor
f(1) = 0
X = 1 is the root
(x-1) is a factor - 23Factoring polynomials Step 4the formula switches to divide
the original formula by our factor to find the missing term "(?)"
- 24Dividing using synthetic division Step 5
- 25Factoring polynomials Step 6Factor the result from Step 5
- 26Factoring polynomials Step 7Final result is all the factor together
X = 1, X = -1/2, X=6
#of roots = # of degrees
- 27Factoring polynomials TYPE 2
- 28Factoring polynomials TYPE 3
- 29rational functionsthe quotient of two plynomials
- 30what degree does it have? Domain?top has degree of "1"
bottom has degree of "2"
Domain {x| x ≠ 2 or x ≠ -2}
Vertical Asymptotes are x=2, x=-2
- 31Are these domains the same?No they have different domains
- 32Are the domains the same? What are they?Left: {x| x ≠ 2 or x ≠ -3}
Right: {x| x ≠ -3}
The canceled term will be a hole on the graph at x = 2
Vertical Asymptote: x=-3
- 33Find Vertical Asymptote1) Factor equation
2) Simplify if needed
3) look for holes
4) Vert Asym will be things denominator cannot be equal to - 34Find Vertical Asymptote Holes Rules1) Cancel like terms on NUM and DENOM
2) Simplify expression
3) plug cancelled x-value into equation
4) dont confuse with factor value - 35Find Vertical Asymptote Holes 1
- 36Find Vertical Asymptote Holes 2
- 37Find Vertical Asymptote Holes EXAMPLE. Solve
- 38Horizontal Asym Rules
- 39No horizontal AsymtopePossible Oblique Asym
Check for top power to be one more than the bottom power.
- 40Oblique Asymcubic divided by quadriatic
Oblique Asym is a linear Line - 41Can you cross the vertical asym?No
- 42Find y int on rational function
Informationen
- Beschreibung
- Karteikarten am MTH107-3, erstellt von Bob Harold am 18/10/2019.
- Erstellt von
- Bob Harold
- Aufrufe
- 20
- Bewertung