1.2 : INTRO TO RELATIONS AND FUNCTIONS
Terminology
1. Interval notation vs set-builder notation vs graph (number line)
Ex. Write using interval notation and graph
a) cfw_x | x -3
b) cfw_x | -5 < x -4
Ex. Write using set-builder notation
a) [ 2, 7)
b) (3
2.2 - 2.3 Transformational Graphing
(2.2) Horizontal and Vertical Shifts
Explore: Graph each function
a) y = x2
b) y = x2 + 3
c) y = x2 2
d) y =
e) y = + 2
f) y = - 4
Observation:_
So, f(x) can be translated up or down by adding or subtracting c on the O
2.6 Functions and Composition
Add/Subtract: (same as adding or subtracting polynomials)
f + g = (f + g) (x) = _
f g = (f g) (x) = _
Multiply
fg = (fg) (x) = _
Divide (Restrictions on domain exist because of variable in denominator!)
= () (x) = _
Ex.
(f+g)
Section 2.1
Graph of basic functions
Continuous:_
Increasing, decreasing, constant: _
Determine the largest interval of the domain over which the function is
continuous.
Determine intervals of increasing, decreasing, constant, and domain/range.
Library of
Notes 3.2 3.3
K. Lee
Quadratic Equation:
Standard Form:
f(x) = _
Vertex Form:
f(x) = _
Vertex (
,
)
Axis of symmetry - x = _
Direction is determined by the _ value
Min/Max is at the value of y = _
MAT110
Methods for graphing:
D - _
A - _
V - _
I - _
S - _
3.1 Complex Numbers
Complex numbers are made up of the _ and
_.
Imaginary Numbers Review
By definition: i = _
So.
i2 = _
i3 = _
i4 = _
*This pattern repeats every 4 powers
Simplify:
Ex. i8
Ex. i19
Ex. i42
Ex. i-15
Complex Numbers
a + bi
Real part - _
Ima
3.4 NOTES APPLICATIONS OF QUADRATICS
1) Find the max value of y = -2x2 + 8x 5
2) Suppose x represents one of two positive numbers whose sum is 45. For
what two such numbers is the product equal to 504?
3) A golf ball is hit so that its height h in feet af
Section 7.1: Rational Functions and Simplifying Rational Expressions
What are rational numbers? _
Objectives:
Find the domain
Simplify Rational Expressions
Find the value of a rational function
Find the domain of a rational expression.
What happens when y
Review of Factoring (part 3) and Solving by Factoring:
Section 6.4: Factor Trinomials by Grouping AND Slide and Divide
Remember:
Three terms (trinomial)
+C
_ to get middle
_ signs
-C
_ to get middle
_ signs
+ +
2 + 14 + 8
2 13 + 7
A not 1
AND we cant
Section 4.5: Problem Solving using Systems of Equations
What is the first thing you do when you are given a Word Problem?
(skip it is NOT the correct answer!)
1) _ to determine the _ of word problem.
2) Read it again to label your variables. Now you know
Section 4.3: Solve Systems of Equations by ADDITION (Elimination)
Why do we need a third way to solve systems?
Because this is Mrs. Kitts FAVORITE! Also, remember the last example from
Section 4.2?
5 + 10 = 20
2 + 6 = 10
It was a pain to work. Why? _
When
Section 4.2: Solve Systems of Equations by SUBSTITUTION
Why do we need another way to solve systems? Remember the solution to a
system of equations is where the two lines cross.
Here are some possible answers: (
3
17
,
5
11
) (4.312, -7.754)
Those answers
Section 10.3: Simplifying Radical Expressions
Objectives:
Multiply Radicals
Divide Radicals
Simplify Weird Radicals
Multiply.
= _ _ = _
OR:
= = _
So.when multiplying radicals where the index is the same just put them under
the same _ .
Examples:
.
.
.