Definitions

Question 1

Inverse functions

Answer 1

When the x and y values are switched.

*functions only have inverses if they are one-to-one

Question 2

Identity function

Answer 2

The function that maps every element of the domain to every element of the range

*simple def-the x value is the same as the y value

Question 3

Composition of functions

Answer 3

When two or more functions are evaluated at the same time. The two function will always be given to you and all you need to do is determine which one to evaluate first.

Notations (there are two)
F(g(x)) means f of g of x, which means evaluate g(x) first and then evaluate that result using f(x)

Question 4

Inverse variation

Answer 4

When two numbers are proportional.
*written as a fraction
Y=a/x  
a doesn't equal 0 
Xy=a
 a is the constant of variation and y is said to vary inversely with x

Question 5

Inverse variation ex.

Y varies inversely as x. If, y=6& x=-3, find y when x=4

Answer 5

Step 1: write inverse variation equation.
Step 2: substitute -3 for x & 6for y
Step 3:solve for a
Step 4: write an equation that relates x& y
Step 5:substitute 4 for x
Step 6: reduce

Question 6

What is the general equation of a circle? (aka center-radius form)

Answer 6

(x-h)squared+(y-k)squared=r squared

R is the length of the radius and(h,k) is the center of the circle.
***note the h and k are opposite signs in the equation.

Question 7

General form

Answer 7

X squared+ y squared+Dx+Ey+F=0

Where: D=-2h E=-2k F=h squared +k squared-r squared

Question 8

Solving quadratic equations

Answer 8

Steps:

1. Write in standard form and set equal to zero.
2. Factor
3. Set each parenthesis equal to zero and solve.
4. Check each answer.

Question 9

Solving quadratic inequalities

Answer 9

Steps:

1. Get into standard form
2. Factor
3. plot number(s) on number line
4. Test values in each section

Question 10

Simplify rational expressions with factorable parts

Answer 10

Steps:

1. Factor both numerator and denominator.
2. Reduce any terms that are exactly the same to one.
3. Reduce any terms that are opposite AND subtraction to (-1)
4. Reduce any GCF coefficients.