1. 19A-19E Cubic, Quartic, and Rational Functions
Unit 4: Mathematical Models
19A, 19B, 19C, 19D, 19E
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2. Example classification: polynomial, cubic y-int: x-int(s):
19A, 19B, 19C, 19D, 19E
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3. Cubic Functions can be used to model volume degree: 3
maximum number of turns: 3 – 1 = 2
opposite end behavior
if a > 0 then left: falls right: rises
a < 0 left: rises right: falls
domain: range:
19A, 19B, 19C, 19D, 19E
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4. Quartic Functions degree: 4 maximum number of turns: 4 – 1 = 3
same end behavior
if a > 0 then left: rises right: rises
a < 0 left: falls right: falls
domain:
range: depends on end behavior and minimums/maximums
19A, 19B, 19C, 19D, 19E
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5. Rational Functions
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comprised of polynomial functions g(x) and h(x) with a vertical shift k
n: degree of numerator g(x)
m: degree of denominator h(x)
zeros of h(x) are: restrictions to the domain of f(x)
vertical asymptotes (set equal to x)
If n = m then horizontal asymptote of
n < m horizontal asymptote of y = 0 + k
n > m no horizontal asymptote
n = m has a slant asymptote
19A, 19B, 19C, 19D, 19E
5/8/ :00 PM

6. Guided Practice
p. 545: 1-2 p. 549: 1, 2cd p. 552: 1c, 2 p. 554: 1, 4a, 5 p. 555: 2ag Read and follow all instructions. List the page and problem numbers alongside your work and answers in your notes. Use the back of the book to check your answers.
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19A, 19B, 19C, 19D, 19E
5/8/ :00 PM