Unit 1 Review
1. Relations and Intervals
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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
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
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
1. Linear Function
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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
2. Linear Function
• Two parallel lines: equal slopes
• Perpendicular lines: m1×m2 = -1
• Linear Regression
exercise
• Skills test 1: #4
• Skills test 1: #8
• Skills test 1: # 10
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)
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
exercise
• Exam review: # 6
• Exam review: # 8
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
exercise
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Skills test 1: # 29
Skills test 1: #30
Exam review: #13
Exam review: # 14
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
exercise
• Exam review: #16
• Exam review: # 17