Functions:

Domain and Range Examples:

Give Domains and Ranges of the following:

{(1, 0), (1, 1), (1, 2), (1, 3)}

{(2, 3), (4, 10), (5, 100)}

Name values not in the domain of the following:

1/x
sqrt(x² - 3)

Given f(x) = x², and g(x) = x+3, find:

f(g(x))
g(f(x))

Determine if the functions are inverses of each other:

f(x) = x - 3
g(x) = x + 3

Find the inverse of the functions:

f(x) = x³ - 3
f(x) = 2x + 3

Find the Zeros for the following functions:

f(x) = 3x + 3
f(x) = 9x - 3

Find the distance between these points:
(3, 5),(5, 5)
(8 , 3), (3, 65)

Find the perimeter of the triangle having vertices at these coordinates:

(3, 3), (3, 6), (4, 6)

Write the equation in slope-intercept form for a line which passes through the points:

(3, 5), (3, 1)
(3, 6), (65 , 4)

Find the slopes of the following equations:

3x+3y = 39
5x-35y = 5

Systems of Equations:

Is the following coordinates the answer to the system of equations:

(0.5, 5)
y = 3x
y = 4x

Matrices:
3 5 6 3 9 0
a= 4 5 4 b = 4 4 2
3 3 3 0 1 0

a*b
b-a
a+b

Polynomials

Find the value of c to make perfect squares:

x² + 3x + c

Solve each by completing the square:

x² + 6x + 9 = 0
x² + 6x + 8 = -30

Solve each equation by quadratic formula:

x² + 33x - 89 = 8

Trigonometry

Trigometric Functions

Determine the quadrant the angle lies:
3pi
200 degrees
5/6*pi

Change radian measure to degrees:
pi/3
2pi

Change Degrees to radians(values are in degrees)
210
30

Find the values of the six trig functions for the following coordinates:
(5, 2)

Exact Value:
csc(pi)
sec(30 degrees)
tan(3)

Solve the following with the Law of Sines
A = pi
B = 2/3 pi
a = 3
Find b

Find the amplitude of the following:
Y = 2sin(theta)
Y = 3cos(theta)

Find the Period for the following:
Y = sin(3*theta)

Find the phase shift for the following:
y = tan(theta)

Write the following as an inverse relation:
x = sin(theta)
y = cos(theta)

Evaluate:

sin(asin(5))
atan(tan(3))

Find the value of the following:

atan(1)
acos(3)

State domain of the following:
y = cos(theta)
y = cot(theta)

Solve with sum/differences:
sin(195 degrees)

Polar Coordinates

Convert Polar Coordinates to Rectangular:
(3, pi)

Simplify:
i² + i⁸

Conics:

Find the Radius of the circle and center coordinates:

(x - 2)² + (y + 3)² = 9
(x + 1)² + (y +1)² = 16

Exponents and Logarithmic Functions

Rational Exponents

Evaluate:
4⁶
121^0.5

Express using rational Exponents:
(a⁴*b¹⁰)^0.5
(a⁹*b⁷*c⁵)^1/3

Simplify:
4x²*(4x)²-2

e:

Evaluate:
e²

Logarithmic Functions

Write each equation in logarithmic form:
2⁴ = 16

Write each equation in exponential form:
log₂(8) = 3

Evaluate each expression:
log₉(9)⁶

Limits

Evaluate:
Lim 6x=y as x ->2
lim (25 - x²)^0.5 as x -> 5

Derivatives

Find the derivative of each function:
f(x) = 4x
f(x) = x² - 2x + 1