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Unit 3 - Polynomial Fucntions , Expressions , Equations - Coggle Diagram
Unit 3 - Polynomial Fucntions , Expressions , Equations
tranformations
:heavy_minus_sign: f(x) :left_right_arrow: reflected on the x-axis
f( :heavy_minus_sign:x) :left_right_arrow: reflected on the y- axis
outside the () parenthese :left_right_arrow: vertical shift easy
inside the () parentheses :left_right_arrow: horizontal shift easy
f(ax) 1. if a>1 = horizontal compression by a factor of 1/a
if a<1 - a fraction = horizontal stretch by a factor of a
a f(x)
1. if a > 1 = vertical strech
if a < 1 = vertical compression
Inverse of functions
:one:swap f(x) with y :two: solve for x :three: switch x with y
:four: repalce y with the inverse sign thing
Cubic fucntions
points are (0,0), (1,1), (-1,-1)
transformations are the same with the above
basics
coefficients -- leading coefficient the one next to the greatest power
degree - power
end behaviour == As x → −∞, P(x)→+∞ and as x→+∞, P(x)→ −∞ :warning:
Binomial Theorum
the triangle thing for nCr infront of each monomial in the multiplying process
eg. (x+y)^4 = 4C0 x^4 y^0 and ect.
the complicated formula with P(r)= nCr P^r q^n-r
factoring polynomials
find common factors - factor out the common factors in each group and factor agian
dividing polynonmials
synthetic division refer to the brightspace thing or search online
long division
conjugate just change the middle sign like 2i+1 is 2i-1
rational solutions - factor and then equate each factor to 0 to get the roots
