Relations and Functions
Linear Functions
Linear Transformations
Arithmetic Sequences
Scatterplots and Lines of Best Fit
1
Is the following relation a Function?
(1,3) (5,6) (4,2) (-4, 5) (0, 6)
It is a Function.
1
Evaluate the function f(x)=3(x+5)-17
when x=3.
f(3)=7
1
When you have a number is being added or subtracted to INSIDE the parantheses, it's this kind of transformation.
Horizontal Translation
Horizontal Shift
1
Is the following Sequence Arithmetic?2,6,10,14,18,24,28,32
It is Not!
1
As time passes, the temperature during the day decreases. This describes THIS kind of Association.
Negative Association
2
Write the Domain and Range of the following relation.
(2,3) (5,-1) (-3, 9) (-4, 5) (0,1)
Domain: {-4, -3, 0, 2, 5}
Range: {-1, 1, 3, 5, 9}
2
Write the linear function for the data in the table.
x=3,4,5,6,7,8
y=12,15,18,21,26,29
This is not a Linear Function.
2
When you have a number adding to the entire output of the function, you get THIS kind of Transformation.
Vertical Translation/Vertical Shift
2
Write the recursive formula and find the first 5 terms with the following info.
a1=12, d=7
a1=12
an=an-1+7
12,19,26,33,40
2
The more time you study, the higher your grade could be. This describes THIS kind of Association.
Positive Association
3
Is the following relation a function? If so, is it One-to-One?
(7,5) (-4,5) (13, 13) (-9,-9) (2,8)
The relation is a Function, but is not One-To-One.
3
Sketch the graph of the linear function.
y=(5/2)x-3
Look at the board.
3
When you multiply the function by anything bigger than one, it is THIS kind of transformation.
Vertical Stretch
3
Write the explicit formula using the following recursive formula.
a1=8, an=an-1+15
an=-7+15n OR an= 8+(n-1)(15)
3
As the x values increase, the y-values jump up and down all over the place. This describes THIS kind of Association.
No Association
4
Is the following graph a function?
It is not a function.
4
Write the linear function for the data in the table.
x: 0, 1, 2, 3, 4
y:-1, 4, 9, 14, 19
y=5x-1
4
Identify the transformations that happen from f(x) to g(x).
f(x)=x, g(x)=2x-4
Vertical Stretch by factor of 2
Vertical Shift 4 units down
4
Use the Explicit Formula to find the Recursive Formula.
an=3+6n
a1=9
an=an-1+6
4
As the x-values increase, the y-values decrease by 3 units each time. A linear relationship is modeled. What type of correlation does this describe?
Negative Correlation
5
Identify the Domain and Range of the following function.
Domain: All real numbers
Range: All real numbers
5
Evaluate the function f(x)=(-1/3)x+13
When x=-3.
f(-3)=14
5
Identify all of the transformations that occur from f(x) to g(x).
f(x)= x , g(x)=1/3(x+2)+5
Vertical Compression by factor of 1/3.
Horizontal Shift 2 units left.
Vertical Shift 5 units up.
5
Write the recursive Formula using the following Explicit Formula.
an=108-n
a1=107
an=an-1 -1
5
For the table below, determine the trend line and write its equation.
x: 2,4,6,8,10
y: 3,6,9,12,15
y=(3/2)x