Quiz 1B Math

Horizontal Case 1

the leading terms have the same degree (n=d)

result: horizontal asymptote that is the ratio of the leading term coefficients y= a/b

Horizontal Case 2

the denominator dominates the numerator (n<d)

result: horizontal asymptote of y=0

Horizontal Case 3

the numerator dominates the denominator (n>d)

result: NO HORIZONTAL ASYMPTOTE

y=x

y = x²

y=x³

y= 1/x

for rational funcs the denominator

can’t equal 0

Degrees divided

subtraction

Special cases

the degree of the numerator is exactly 1 more than the degree of the denominator

result: oblique(slant) asymptote

Slant asymptote is long division (ignore remainder)

vertical asymptote

set denominator equal to zero

BUT if the factor cancels out its a hole

finding x-intercepts/zeros

this will be found in the numerator

when finding domain for rational functions

ALWAYS at the denominator for this info

Binomial theorem

(a+b)²= (a+b)(a+b)= a^²+2ab+ b²

Pascel triangle hint

when you choose what row you’re using label each first variable from greatest to least

label each 2nd variable from least to greatest

ex. (x+2)² would be mean the 2nd “variable is 2” and the 1st one is x

Additive: Vertical translations (k)

up+k or down-k

Additive: Horizontal translation (h)

(x+h) or (x-h) then you flip sign

Multiplicative: Vertical (a)

Vertical dilation by a factor of a is simple multiplication

Multiplicative: Horizontal (b)

Horizontal dilation by factor of 1/b ( divide by b)

g(x)= f(bx)

note: b is inside

a-value

vertical reflection across x axis for a<0

vertical dilation by factor of a

(x-a)²

bounces (quadratically)

(x-a)³

squiggle (cubically)

odd degree (x³)

end behavior opposite

even degree (x²)

end behaviors are the same

positive leading coefficients

up on the right

negative leading coefficients

down on right

transformations of polynomial function

F(x)= a f[b(x-h)]+k