Complex numbers
System of equations
functions
Difference Quotient
Domain
Composition function
Transformations
100
what does i^2 equal to?
i^2=-1
100
Describe the three methods to solve system of equations
Graphing: Graph the two equations and find the point of intersection
Substitution: solve one equation to be x/y=..., then plug in that equation into the second one and solve
Elimination/Addition: Multiple one or both equations so you can subtract or add the equations together and completely eliminate a variable.
100
What test is used to see if a graph is a function?
Vertical line test
100
find f(a) for the following function:
f(x)=x^2+2x-1
f(a)=a^2+2a-1
100
What are the restrictions for fractions and radicals?
The denominator of fraction cannot equal zero
in 1/x , x!=0
The inside of radicals cannot be negative
in sqrt(x) , x>=0
100
What is the symbol that is associated with composite function
∘
used as (f∘g)(x)--->f(g(x))
100
What is the general equation showing tranformations?
Hint: Also called vertex point equation
f(x)=a(x-h)^2+k
200
What is the conjugate of -1+4i
-1-4i
200
Solve the system of equations using substitution
{(3x,+,y,=,11),(x,+,y,=,7):}
(2,5)
200
Is this a function? Explain why or why not
It is a function
200
Find f(a+h) from the following function:
f(x)=x^2-3x+5
a^2+2ah+h^2-3a-3h+5
200
Write the interval notation for the following function:
1/(x^2-6x-27)
x!=9, -3
(-oo,-3)uu(-3,9)uu(9,oo)
200
find f(g(x)) using the following functions:
f(x)=2x-1
g(x)=1/2x+2
f(g(x))=x+3
200
Which of these graphs represent an absolute function graph?
A. 
B. 
C. 
D. 
C
300
Solve and simplify
(5+3i)/(2-i)
7/5+11/5i
300
Solve the system of equations using graphing
{(y,=,-2x,+,4),(2y,=,-4x,+,8):}
(x, -2x+4)
300
Describe how we determine if an equation is a function using inputs and outputs
One input (x) can not have more than one output (y)
300
find f(a) and then f(a+h) for the following equation:
f(x)=2x^2-6x-7
f(a)=2a^2-6a-7
f(a+h)=2a^2+4ah+h^2-6a-6h-7
300
Find the interval notation for the following function:
f(x)=(x^2-2x-3)/(sqrt(-4x+3))
(-oo, 3/4)
300
Find f(g(x)) using the following functions
f(x)=5x-7
g(x)=2x^2-3
f(g(x))=10x^2-22
300
Graph the following transformation
f(x)=|x+3|-2
400
Solve and simplify
(7-2i)/(3+2i)
17/13-20/13i
400
Solve the following system of equations using substitution:
{(3y,=,x,+,7),(4x,-,5y,=,14):}
(6,11)
400
Does this graph pass the vertical line test?
Yes, it is a function
400
Evaulate the following function for
(f(a+h)-f(x))/h
f(x)=3x+2
3
400
Write the interval notation for the following function:
root(3)(x^2+2x-3)
(-oo,oo)
400
Find f(g(x)) using the following equations:
f(x)=x^2-15
g(x)=sqrt(13-x)
f(g(x))=-x-2
400
List the transformation and graph the following function:
f(x)=-2(x+3)^2
Flip across x axis
Stretch horizontally by 2
Shift left 3 units
500
(1-5i)/(sqrt(-36)-4)
-17/26 + 7/26i
500
Solve the system of equations using elimination:
{(6x,-,9y,=,15),(10x,-,15y,=,25):}
(x, 2/3x-5/3)
500
Does this graph represent a function?
Yes, this graph passes the vertical line test. The point (2,1) is not filled in, meaning the point is not included
500
Evaulate the following function for
(f(a+h)-f(x))/h
f(x)=4x^2 - 7x + 3
8x+4h-7
500
Find the restriction for the following function and write the domain in interval notation
f(x)=(sqrt(9-x))/(x^2-4x-5)
x<=9
x!=5
x!=-1
(-oo,-1)uu(-1,5)uu(5,9]
500
Find f(g(x)) using the following equations
f(x)=1/(x+6)
g(x)=8/x-6
f(g(x))=x/8
500
List the transformations and graph the following function:
f(x)=-sqrt(x+3)-5
flip across x axis
shift left 3 unitS
shift down 5 units