Pre-Calculus: Chapter Three

Front 1

Quadratic Function

Back 1

Ax^2 plus or minus Bx^2 plus or minus Cx^2

Front 2

The Degree of the Polynomial

Back 2

The highest power

Front 3

Leading Coefficient Test (L.C.T.)

Back 3

Find the multiplyer with the highest power.
If even, it's a parabola.
If odd, it's a vertical s-shaped

Front 4

Multiplicty Test

Back 4

If an even amount, it touches the x-intercept.
If an odd amount, it crosses the x-intercept.

Front 5

Steps in Graphing a Function

Back 5

1) Name the x and y intercepts
2) Perform the L.C.T.
3) Perform the Multiplicity Test
4) Graph the function

Front 6

Finding Vertical Asymptote

Back 6

Factor out the denominator and set it equal to 0

Front 7

Finding Horizontal Asymptote

Back 7

1) If degree on top is less than the degree on bottom, then the asymptote is y=0
2) If the degree on top is more than the degree on bottom, then divide the numerator by the denominator
3) When the degrees equal, then the leading coefficient on top over the leading coefficient on bottom is the asymptote

Front 8

Finding Horizontal Asymptote

Back 8

1) If degree on top is less than the degree on bottom, then the asymptote is y=0
2) If the degree on top is more than the degree on bottom, then divide the numerator by the denominator
3) When the degrees equal, then the leading coefficient on top over the leading coefficient on bottom is the asymptote

Front 9

Real Zero Theorem

Back 9

A polynomial function cannot have more zeros than it's degree

Front 10

Remainder Theorem

Back 10

If f(x) is a polynomial and f(x) is divided by x-c, then f(c)=r, where c is a constant

Front 11

Possible Zeros

Back 11

To find all possible zeros, take ll factors of the leading coefficient and the smallest coefficient

Front 12

Intermediate Value Theorem

Back 12

If f is continuous on the interval [a,b] and c contains the element of [a,b), then f(a) and f(b) are between k. Then, there exists a c such that f(c)=k

Front 13

Intermediate Value Theorem Format

Back 13

Clearly f(x) is continuous
f(_)=_
f(_)=_
Since f(_) is less than/greater than 0 and f(_) is less than/greater than 0, then there exists a c that contains the element of [_,_] such that f(c)=0