Domain and Range
What values are the domains and which are the ranges?
Domain= x-values
Range= y-values
Find the value of f(x)= 4x+10 when x= -2
f(x)=2
Compare f(x) and g(x) below. What transformation is taking place?
f(x)=-7x+9
g(x)=-7(x+2)+9
shift left 2 units
How do you know if a sequence is arithmetic?
There is a common difference.
Describe what a graph looks like for the following:
positive correlation
negative correlation
No correlation
Positive: x & y values increase; the scatter plot goes in an upwards direction with a trend line
Negative: x & y values decrease; the scatter plot goes in a downwards direction with a trend line
No: there is no general direction that the points follow
What is the domain and range of the following points?
(2,4) (6,-3) (5,-2) (7,4)
D: 2,6,5,7
R: 4,-3,-2
Find the value of f(x)= -3x+5 when x= -4
f(x)=17
Compare f(x) and g(x) below. What transformation(s) is taking place?
f(x)=x
g(x)= x -5
shifted 5 units down
Is the following sequence arithmetic or not? If it is arithmetic, what is the common difference?
-9,-3,3,9,15
it is arithmetic
d=6
The average monthly heating bills for houses in a neighborhood are positively correlated to the number of pets in the house. Can it be inferred that the number of pets in a household causes an increase in average monthly heating bills? Explain.
No, to determine if this is a causal relationship, you must conduct an experiment that can control the other variables that might influence the relationship.
How do you know if a relation is a function or not?
If the x-values repeat it is not a function
Find the value of f(3) for the function f(x)=-2x+7
f(x)=1
Compare f(x) and g(x) below. What transformation(s) is taking place?
f(x)=3x+4
g(x)= 2(3x)+4
horizontal compression
Write an explicit formula for the following sequence. Use the formula to find the 32nd term.
{4.5,9,13.5,18}
an= 4.5+4.5(n-1)
a32= 144
Based on the information below, write a linear regression, determine what r is and also describe the correlation.
x:1 3 4 5 6 8 9
y:17 12 12 10 8 3 1
y= -1.96x+19.1
r= -0.99
Strong negative correlation
(-2,4)(3,2)(2,1)(4,7)(3,-5)
No because the 3 repeats
Find the value of f(-5) for the function f(x)=3x+7
f(x)= -8
Compare f(x) and g(x) below. What transformation(s) is taking place?
f(x)=4x - 5
g(x)= 2(4x-5)
vertically stretched
Convert the following formula to recursive.
an=13-4(n-1)
a1=13
an=an-1 -4
Based on the information below, write a linear regression, determine what r is and also describe the correlation.
x:3 4 5 6 7 8
y:12 5 6 8 9 11
y=0.26x+7.09
r= 0.18
weak correlation
Determine a reasonable domain and range.
Jamie works at least 5 hours a week after school and she earns $9.25 an hour. Compare the relationship between the number of hours works and the total amount earned.
D: # of hours works >5
R: multiples of 9.25
Write a linear function (equation) for the data below.
x: 0 1 2 3
y: 3 -1 -3 -5
f(x)=-4x+3
Compare f(x) and g(x) below. What transformation is taking place?
f(x)=4x
g(x)= (4x-3)+2
shift up 2 and a right 3
Based on the following sequence, write a recursive and explicit formula.
{12,19,26,33}
explicit: an=12+7(n-1)
recursive: a1=12
an=an-1 +7
Based on the information below, write a linear regression, determine what r is and also describe the correlation and then graph the equation on your calculator.
x:3 7 9 13 15 21
y:12 15 21 13 25 27
y=0.79x+9.9
r=0.8
strong positive correlation