Flashcards

MTH107-3

Bob Harold English 42 cards

Cards in this deck (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