Functions and Relations
Polynomial and Rational Functions
Exponential and Logarithm Functions
Matrices and Determinant
Conic Section
100
Determine whether the relation is a function:
{(1,2),(2,3),(3,4),(1,5)}
Not a function (input 1 has two outputs: 2 and 5)
100
Find the zeros of
f(x)=x2−9
x=-3, 3
100
Solve exponential equation
2x=16
x=4
100
Simplify 
100
Find the center and radius x^2 + (y + 8)^2 = 9
what is center being (0,-8)
radius 3
200
Find the domain and range of:
{(−1,3),(0,0),(2,5),(4,5)}
- Domain = {−1, 0, 2, 4}
- Range = {0, 3, 5}
200
Factor completely
x2+5x+6
(x+2)(x+3)
200
Solve using logarithms
3x=20
x≈2.73
200
Identify element a23 from A =
What is a23 = 2
200
Find the vertices:
y2/16 - x2/36=1
(0,4) and (0,-4)
300
Function value
If f(x)=2x+3, find f(4)
f(4)=2(4)+3=11
300
What is the end behavior of:
f(x)=−2x3+x
- As x→∞, f(x)→−∞
- As x→−∞, x→∞
300
A population grows as
P=200(1.1)t
Find the population after 3 years.
266.2
300
What term do we use to describe a matrix that places a column of constants in the same matrix as the coefficients.
Augmented Matrix
300
Where is the center of the ellipse?
(x-2)2/9 + (y-1)2/4=1
(2,1)
400
Evaluate a function
Given g(x)=x2−1, find g(−3)
g(−3)=(−3)2−1=9−1=8
400
Simplify
(x2−9)\(x - 3)
x+3, where x≠3
400
Convert to exponential form
log2(8)=x
2x=8
400
What is the formula for the determinant of a 2x2 matrix?
[ a b ]
[ c d ]
What is ad - bc?
400
Is the graph a parabola, circle, ellipse, or hyperbola?
x2 + 25y2=50
Ellipse
500
Does the graph of a circle represent a function? Explain.
No, because it fails the vertical line test (one x-value has multiple y-values)
500
Find the horizontal asymptote of
f(x)=(2x+1)/(x−3)
y=2
(same degree → ratio of leading coefficients)
500
Evaluate logarithm
log10(1000)
3
500
Evaluate the determinant of
[ 6 -2 ]
[ 5 1 ]
What is 16?
500
Locate the foci of the equation:
x2/4 - y2/1 =1
(±sqrt(5),0)