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Aim # 10

If the original (parent) function is y=f(x) then

y=cf(x) is the graph of y=f(x) stretched vertically if c> 1

y=cf(x) is the graph of y=f(x) compressed vertically if

0

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( ) () () ( )

( ) ()

Aim #14

Piece-wise function: a combination of one or more functions. The rule is different

for different pieces of the domain.

() { Step function: a piece wise function that is constant over each interval in its

domain (see graph above)

Aim #15

Changing functions to piece-wise function

() || () { () | | () {

()

|| () {

() | | () {

Aim #16

7/25/2019 Review for Math Test 2

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Greatest Integer Function (Floor Function)

gives the the greatest integer less than or equal tox

Least Integer Function (Ceiling Function)

gives the the least integer greater than or equalto x

Long Division

Polynomial Function:

Let n be a nonnegatic integer and let be real numbers with () of degree n

Division Algorithim:Let P(x) and d(x) be polynomials where d(x) 0 and the degree of d(x) is less thanor equal to the degree of P(x)

There exists unique polynomials q(x) and R(x) such that the degree of R(X) is less

than the degree of d(x) and,

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()() ()

()() () ()() ()

Long Division

Remainder Theorem:If a polynomial P(x) is divided by x-k, then the remainder is P(k)

Factor Theorem:

A polynomial P(x) has a factor of (x-k) iff P(x) = 0

Aim #18

Multiplicity: A root of multiplicity of k is a root that is repeated k times.