Enh. AP Pre Calc Unit 1B Vocab

Ratio of two polynomials; f(x)=p(x)/q(x), where q(x) is not equal to 0

Any zero of the denominator of a rational function

Equation where there are rational expressions on both sides of the equal sign

1. Cross multiplication

2. Eliminate the denominator

(Rational equations) when inputting your solutions back into the original equation and get DIVISION BY ZERO on either side of the equation

BOBO BOTNO EATS DC; Bigger on bottom → horizontal asymptote of y=0, Bigger on top → end behavior of y= a/b x^n-d, SPECIAL CASE: exactly one bigger on top → slant asymptote, Same degrees → horizontal asymptote of y=a/b

Single point (x,y) where function is not defined; factor in denominator that does factor w numerator

Vertical line graph approaches but never touches, x= #; factor of denominator that doesn’t cancel w numerator

Horizontal line that graph never meets, y=#

Line neither horizontal nor vertical, y=Mx+b

Zeros in numerator

Identify both zeros and undefined values!

Provides info about…

1. Real zeros

2. Vertical asymptotes

3. Holes

4. Domain

Provides information about…

1. Horizontal asymptote

2. End behavior

3. Y-intercept

Use long division! ← only use the quotient part of answer

Helps w binomial expansion; Based off of Pascal’s Triangle; a term starts w degree n and b term starts w degree 0; a term decreases by one degree, b term increases by one degree.

g(x)=f(x)+k →vertical translation by k units; g(x)=f(x+h)→ horizontal translation by -h units

g(x)=af(x) → vertical dilation by |a|; g(x)=f(bx) → horizontal dilation by |1/b|

1. Multiplicative transformations must be performed and listed BEFORE additive transformations

2. Vertically and horizontally oriented transformations don’t affect one another

3. Domain and range of transformation function may be different from original function

Modeling graphs; common component of AP Pre calc