Functions/Relations
Function Operations
Polynomials
Domain/Range
Inverse of Relations and Functions
100
What is a function?
A relationship or expression involving one or more variables.
100
(3x-8)+(8x+1)=11x+7
(3x-8)-(8x+1)=-5x+1
(3x-8)(8x+1)=24x2-61x-8
(8x2+6x)/2x=4x+3
Addition
Subtraction
Multiplication
Division
100
What is a polynomial?
An expression of more than two algebraic terms, especially the sum of several terms that contain different power that contain the same variable.
100
Fill in the blanks:
Sometimes the domain is ___, sometimes it is ___, sometimes it is ___.
Finite, infinite, infinite but not restricted
100
What is inverse relation?
A relation where each point (x,y) of the original relation becomes (y,x)
200
What is a relation?
Between two sets is a collection of ordered pairs containing one object from each set.
200
Answer the following problem:
f(x)+g(x)
x2+3x+5
200
Solve the polynomial:
x2+7x+19=0
No solution
200
Fill in the blanks:
For the domain, determine ___, the graph goes.
For the range, determine ___, the graph goes.
Left to right
Top to bottom
200
How does this affect the domain and range?
The domain and range can be changed depending on what type of relation is done
300
What is domain and range?
Domain: x-values
Range: y-values
300
Answer the following problem:
g(2)/f(-5)
2/5
300
Find the GCF of the terms of the polynomial:
8x2+32x3
8x3
300
(-3,8) means...
(-3,8] means...
[-3,8) means...
[-3,8] means...
Doesn't include -3 or 8
Does include -3 and 8
Does include -3, but not 8
Includes both -3 and 8
300
What is the rule?
(3,4) ----> (-3,4)
(-5,-1) ----> (5,-1)
(7,0) ----> (-7,0)
Rule: (x,y) ----> (-x,y)
400
Explain how functions and relations are similar.
A function is always a relation but a relation is not always a function.
400
Answer the following problem:
f(x)-2g(x)
3x2-12
400
Factor the following polynomials:
3x3+3x2+x+1
(x+1)(3x2+1)
400
This function squares the input and then adds triple the input.
4=x2+3x
400
How is an inverse function created?
It is created by switching the x and then solving for y
500
Name ordered pairs.
Tables, graphs, regular ordered pairs
500
What are the formulas to the following operations?
Addition
Subtraction
Multiplication
Division
(f+g)(x)=f(x)+g(x)
(f-g)(x)=f(x)-g(x)
(f*g)(x)=f(x)*g(x)
(f/g)(x)=f(x)/g(x)
500
Assume f(x)=-7x-5x4+5 and g(x)=7x4+5+9x, find f(x)+g(x)
2x4+2x+10
500
What is the domain and range?
Domain: (-3,1]
Range: [-4,0)
500
What is the inverse of the following function?
y=2x-1
1/2x+1/2=4