Vocab Pc#2

A² + B² = ?

=( a+b) (a - b)

a² + b² is …..

Prime

a² +2ab+ b² =

(a+b)²

a² - 2ab+ b² =

(a-b)²

a³+ b³ =

( a + b) (a² - ab + b²

a³- b³ =

( a - b) (a² + ab + b²)

Domain

Input (x)

Range

Output (y)

Increasing if a < b

f(a) < f(b)

Decreasing if a < b

f(a) > f(b)

Concave Up:

Rate of Change is Increasing

Concave Down

Rate of Change is Decreasing

Average Rate of Change on [a, b] AND SLOPE OF A SECANT LINE

Average Rate of Change = (f(b) - f(a)) / (b - a)

Degree in Standard Form:

Highest exponent

Degree in Factored Form:

Sum of exponents

Local Min: 1)

Polynomial changes from decreasing to increasing

Local Min: 2)

At a left endpoint where the polynomial is increasing

Local Min: 3)

At a right endpoint where the polynomial is decreasing

Local Max: 1)

Polynomials changes from increasing to decreasing

Local Max: 2)

   At a left endpoint where polynomials are decreasing

Local Max: 3)

At a right endpoint where polynomial is increasing

Absolute Max

largest y-value

Absolute Min

smallest y-value

Point of Inflection

when concavity changes signs

End Behavior (Even)

have the same end behavior

End Behavior (Odd)

have the opposite end behavior

Odd-Degree Roots

“cut” through the x-axis

Even-Degree Roots

bounces” on the x-axis

Even Function:

f(-x)= f(x)

Odd Function:

f(-x)= -f(x)

Positive Right End Behavior:

As x approaches infinity f(x)= infinity

Negative Right End Behavior

As x approaches infinity f(x)= Negative infinity

Positive Left End Behavior:

As x approaches Negative infinity f(x)= infinity

Negative Left End Behavior:

As x approaches Negative infinity f(x)= Negative infinity

Horizontal Asymptote at y = b if:

As x approaches Negative Infinity or positive Infinity f(x)= b

Vertical asymptote at x=a if:

As x approaches plus or minus a f(x)= plus or minus infinity

r(x) =

p(x) over q(x)

p(x)=0 and q(x)=0

False q(x) is Not equal to zero

P(x) and q(x) =0

True

Slant Asymptote if  is 1 degree higher than:

higher than q (x)