what do we look for to determine if a graph is a function? vertical line test what do we look for...

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