Math Midterm 2: Rules to Remember

Leading Term

The highest exponent in the term

Leading Coefficent

The normal number attached to the highest coefficient

Leading Term

everything including the number, the x, and the highest exponent

Finding the VA

A vertical asymptote is the zeros of the denominator: Factor and find the zeros

A ‘hole’

there is a hole when the numerator and the denominator share a common factor: Find that common factor’s zero

Horizontal Asymptote Rules

1. When the highest degree of numerator is less than the highest degree of denominator: y=0

2. When the highest degree of numerator and the highest degree of the denominator are equal: use the leading coefficients instead

3. When the highest degree of the numerator is greater than the highest degree of the denominator: This means there is no HA rather a SA

Slant Asymptote

Finding a slant asymptote means doing Polynomial Long Division and the solution to the division is the solution for your SA

Polynomial Long Division

1. You divide the leading term of the numerator by the leading term of the denominator

2. You multiple the answer in number one by the denominator in the original equation

3. You take your answer in number one and subtract it from the numerator in the long division

4. You take the NEW leading term from number three and divide it by the leading term of the original denominator

5. you take this answer in four and then multiply it by the original equation in the denominator

6. Once again, subtracting the answer in five from your equation in step three

7. Summary: Leading Term/ Leading Term, Multiply, Subtract, Repeat

When do you stop dividing

When the leading term from the equation getting divided is smaller than the original denominators leading term

Rule of Zero in the Denominator

You can never zero out the denominator

When do you use open circles vs brackets

1. Open Circles when there is a < or > sign only

2. Brackets when there is a less/greater than and equal to sign

3. Remember the rule of zeroing out the denominator

Finding the Domain of the Rational Function

It is all based on the zeros of the numerator and denominator. However, you use open brackets for zeros of the denominator

When do you use question marks and zeros in the sign chart

The sign chart helps to visualize the domain, you use zeros when it is a zero of the numerator and a question mark for the zeros of the denominator

Testing Points in the sign chart

When you are testing a point in the sign chart, plug it into the original equation and make sure it keeps the original inequality rule valid. When it is valid use a + sign and when it is not valid use a - sign

Rule for Square Roots in the Denominator

They are always greater than or equal to zero, they cannot be negative and in our practice test we ignored it in question three b

One to One

The equation should equal itself when you plug x into it and solve for x: x=x

Steps to Finding the Inverse

1. Make p(x)=y

2. Switch x and y

3. solve for y

Inverse Domain & Original Range

The domain of the original is the range of the inverse

Memorize This for Price Problems

What does the composition mean, it gives us the weekly profit when the system is price at x