EOCT ReviewUnit 1
Functions
Functions
What do we look for to determine if a graph is a function?
Vertical Line Test
What do we look for to determine if a table is a function?
No repeating x - values
Functions Determine if the following are functions:
1) 2)
3) 4)
x 4 -5 8 9 0
f(x) 5 8 3 3 1
x -2 5 9 4 5
f(x) 0 -8 4 6 1
Domain and Range
Domain: all x – values covered by the graph or table
Range: all the y – values covered by the graph or table
x -3 2 4 9 12
f(x) 0 1 8 9 16
Parent Functions
Linear Function
Quadratic Function
( )f x x
2( )f x x
Parent Functions
Cubic Function
Absolute Value Function
3( )f x x
( )f x x
Parent Functions
Rational Function
Square Root Function
1( )f x x
( )f x x
Manipulating Parent Functions
Multiply the function by a number› Bigger than 1 – Stretch (tall and skinny)› Between 0 and 1 – Shrink (short and fat)
Add a number to a function› Shift up the y – axis
Subtract a number to a function› Shifts down the y – axis
A negative sign in front of a function› Reflects the graph over the x – axis (flips)
Max, Min and Zeros
Max: the highest point of a graph Look at the y - axis
Min: the lowest point of a graph Look at the y -axis
Zeros: where the graph crosses the x - axis
Average Rate of Change
Find the average rate of change:
1) Between the two points: (4,6) (-2,3)
2) Use the graph to find the ARC between the following x – values: -3 and -1
2 1
2 1
y y
x x
Sequences
Infinite and Finite
Infinite: sequence does not end
Finite: sequence ends
3,6,9,12,15,...
2,4,8,16,32
Closed Form
Pattern in how the term relates to the term number
2, 4, 6, 8,10,...
1 2 3 4 52
2na n
Find the sequence Find the general definition of the following:
Find the closed form definition of the following:
1,3,7,15,31,...
2, 5, 8,11,14,...
Logic
Conditional Statement
If, then format The “if” part is the hypothesis The “then” part is the conclusion Notation
If a polygon has exactly 4 sides, then it is aquadrilateral.
p q
Converse Statement
Switch the hypothesis and conclusion Notation
If a polygon is a quadrilateral, then it has exactly 4 sides.
q p
Inverse Statement
Negate the hypothesis and the conclusion Notation
If a polygon does not have exactly 4 sides, then it is not a quadrilateral.
p q
Contrapositive Statement
Switch the hypothesis and conclusion Negate the hypothesis and conclusion Notation
If a polygon is not a quadrilateral, then it does not have exactly 4 sides.
q p
Logic Use the following conditional statement to
answer the questions:
If I buy a car, then it will be red
1) What is the conclusion2) Write the inverse 3) Write the converse