1. Unit 1 Review

2. 1. Relations and Intervals
Set-Builder Notation: {x | x>2}
Interval Notation: (2, ∞)
Relation: a set of ordered pairs
Domain and Range: input and output
Determine domains and ranges from graphs.
Function: one to one relation
Independent variable, dependent variable, vertical line test

3. Exercise
Which of the following representations may describe a function?
A. A set of ordered pairs
B. An equation
C. A graph
D. All of these

4. 1. Linear Functions General form: f(x) = ax + b
Zero of a function: f(x) = 0, x is the zero of the function
X-intercept: zero of a function
Y-intercept: value of y when x = 0
Constant function: y = a
Domain, Range of a linear function

5. 1. Linear Function Slope: (y2-y1)/(x2-x1), rate of change
Geometric orientation based on slope
Slope of a vertical line: undefined
Slope-Intercept form: f(x) = mx+b
Point-slope form: y-y1 = m(x – x1)
Standard form: Ax + By = C, A ≠ 0

6. 2. Linear Function Two parallel lines: equal slopes
Perpendicular lines: m1×m2 = -1
Linear Regression

7. exercise
Skills test 1: #4
Skills test 1: #8
Skills test 1: # 10

8. 3. Linear Equation and Inequalities
Addition and Multiplication Properties of Equality
Graphical approaches to solving linear equations: Intersection
X-intercept method: f(x) = g(x) , find the zero of F(x) = f(x)-g(x)

9. 3. Linear Equation and Inequalities
Addition and multiplication properties of inequality
Graph approach: f(x) > g(x)
X-intercept method of solution of a linear inequality: F(x) >0, x such that F is above the x-axis
Three party Inequalities

10. exercise
Exam review: # 6
Exam review: # 8

11. 4. Basic Function and Symmetry
Basic Functions and their domain & range ,get to know their corresponding graphs
Symmetry with respect to the y –axis:
f(x) = f(-x), even function
Symmetry with respect to the x-axis:
not a function, if (a,b) is on the graph, then (a, -b) is also on the graph
Symmetry with respect to the origin:
f(x) = -f(-x), odd function

12. exercise Skills test 1: # 29 Skills test 1: #30 Exam review: #13

13. 5. Transformations Vertical and horizontal shift
Vertical and horizontal stretching and shrinking
Reflection
Basic rules: f(x) = cf(bx + a) + d
order: b, a, c, d

14. exercise
Exam review: #16
Exam review: # 17