17, 13, 9, 5, …1. Write the rule for the above sequence.
2. What is the 12th term?
3. -19 is what term in the sequence?
Coord Algebra Support
UNIT QUESTION: How do we graph functions, and what can be done to change the way they look?Standard:
Today’s Question:How do we find the domain and range of a function?Standard: MM1A1d
Discrete (points) graphsDiscrete (points) graphs
– – you just LIST the domain and you just LIST the domain and rangerange
Continuous (lines or curves) graphsContinuous (lines or curves) graphs
– – you use interval notationyou use interval notation
Domain & RangeDomain & Range
Domain and Range: Points
Find the domain and range:
domain: {2, 3, 4, 6}range: {–3, –1, 3, 6}
{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}
Interval Notation Interval Notation Uses:Uses:
( #,#)
[ #,#]
Are used when there is an open dot or the number is NOT included on the graph.
Are used when there is a closed dot or when the number is included on the graph.
Domain and Range: Graph
:
:
D
R
[ 3,2]
[ 5,2]
Domain and Range: Graph
:
:
D
R
[ 3,3)
( 1,2]
Domain and Range: Graph
:
:
D
R
[ 3,3)
[ 4, 2]
Special case: When there is an open circle and closed circle on the same number – go with the closed circle.
Domain and Range: Graph
:
:
D
R
[ 4, 2]
[ 1,4]
Domain and Range: Graph
:
:
D
R
( -∞,∞)( , 4]
** When there are no dots – assume there are arrows and the graphs continues in that direction
You try!!You try!!
x-interceptx-intercept – the point at which the – the point at which the line intersects the x-axis at line intersects the x-axis at (x, 0)(x, 0)
y-intercepty-intercept – the point at which the – the point at which the line intersects the y-axis at line intersects the y-axis at (0, y)(0, y)
InterceptsIntercepts
ZEROSZEROS are the same thing as are the same thing as thetheX-INTERCEPTSX-INTERCEPTS..
Name the zeros.Name the zeros.
(-4, 0)and
(3, 0)
Name the Y-INTERCEPT.Name the Y-INTERCEPT.
(0, -4)
Increasing & Decreasing
MOVE LEFT TO RIGHT
If your finger is going up, the graph is INCREASING
If your finger is going down, the graph is DECREASING
If your finger goes neither up or down…then the graph is CONSTANT
Increasing and DecreasingIncreasing and Decreasing
To find where the graph is increasing and decreasing trace the graph with
your FINGER from left to right.
Increasing, Decreasing, or Increasing, Decreasing, or Constant?Constant?
1.1. Domain:Domain:
2.2. Range:Range:
3.3. Intercepts:Intercepts: x-int:x-int:
y-int:y-int:
4.4. Increasing or Increasing or Decreasing?Decreasing?
CharacteristicCharacteristicss