Relations and Functions
What is the domain of a function? Give an example.
Domain: All the x-values of a set
How do we write a linear equation in function notation?
f(x) = mx+b
Which transformations affect the slope of the original function?
Horizontal Compression and Vertical Stretch.
a1=
an = an-1 + d
a1 is the first term
an is the term you want to find
an-1 is the previous term
d is the common difference
If a scatter plot has a positive association, what happens to the y-values as the x-values increase?
As the x-values increase, the y-values increase
What is the range of a function? Give an example.
Range: All y-values of a set.
Given f(x) = 6x + 15
Find f(4), f(6), f(8)
f(4) = 39
f(6) = 51
f(x) = 63
How do the following functions compare to f(x) = 3x + 2:
g(x) = 3(x+4) + 2
The function is shifted to the left 4 units.
Write the standard form of an explicit formula. Then label each component.
an = a1 + (n-1)d
an is the term you want to find
a1 is the first term of the sequence
n is the term number you want to find
d is the common difference
If a scatter plot has a negative association, what happens to the y-values as the x-values increase?
If a scatter plot has no association, what happens to the y-values as the x-values increase?
A. as the x-values increase the y-values decrease
B. the y-values can increase or decrease, they do not depend upon the x-values.
What is a one-to-one function? Give an example of a one-to-one function.
A one-to-one function is a function where every x-value relates to a unique y-value.
Write a linear function given the following x and y values
x: 2, 4, 6, 8, 10
y: 4, 8, 12, 16, 20
How do the following functions compare to f(x) = 6x +2:
A. g(x) = 6(2x) + 2
B. g(x) = 6x + 6
A. Horizontal compression by a factor of 2
B. Vertical shift by 4 units up
Write a recursive formula given the following explicit formula. Then find the second and third term.
an = 23 + (n-1)*6
a1 = 23
an = an-1 + 6
a2 =29
a3 = 35
Given the following correlation coefficients, determine the strength and direction of the correlation
A. r = 0.93
B. r = -0.25
C. r = -0.84
D. r = -0.95
A. Strong Positive
B. Weak Negative
C. Strong Negative
D. Strong Negative
Determine if the following are functions, then give the domain and range:
A. {(1,8), (2,7), (3,6), (4,8), (5,7), (6,10), (6,11)}
B. {(2,8), (4,3), (6,6), (8,2), (10,4), (12,9), (14,7)}
A. Is not a function (6 goes to 10 and 11) Domain: {1-6} Range: {6, 7, 8, 10, 11}
B. Is a function (all x-values go to one y-value) Domain: {2, 4, 6, 8, 10, 12, 14} Range: {2, 3, 4, 6, 7, 8, 9}
The Missoula County parking force charges a flat rate of $4.00 for parking. Every hour that goes by after you initially park, you are charge $1.50. Write a linear function for this situation. How much would you be charged for 5 hours of parking?
f(x) = 1.5x + 4
f(5) = $11.50
How do the following functions compare to f(x) = 2x + 7
A. g(x) = 2(x-3) + 11
B. g(x) = 6(2x+7)
C. g(x) = 2(6x) + 3
A. Horizontally shifted right 3 units and vertically shifted up 4 units
B. Vertical stretched by a factor of 6
C. Horizontally stretched by a factor of 6 and shifted down 3 units.
Write a recursive formula given the following explicit sequence. Then find the second and third term.
an = -60 + 10n
a1 = -50
an = an-1 + 10
a2 = -40
a3 = -30Make three different scatter plots. One with a positive association, one with a negative association, and one with no association.
Self Check
Determine the Domain and Range of the following.
Tickets to a sporting event cost $75 each.
The average person walks 2.5 miles per day.
A. Domain: Whole numbers, Number of tickets
Range: Multiples of 75
B. Domain: Whole numbers, Days
Range: Multiples of 2.5
A ski rental shop rents skis for a flat rate of $75. Every day you have the skis, the rental shop charges $25. Write a linear function for the situation, then determine how much it would cost to ski for three days. Then graph the function.
f(x) = 25x + 75
f(3) = $150
How do the following functions compare to f(x) = 4x + 1
A. g(x) = 4x-11
B. g(x) = 6(4x+1) + 2
C. g(x) = 3(4x) + 1
D. g(x) = 4(x+7) + (-1)
A. shifted down 12 units
B. Vertical stretch by a factor of 6, vertically shifted by 1 unit
C. Horizontal compression by a factor of 3
D. Horizontally shifted left 7 units and Vertically shifted down 2 units
Write an explicit formula given the following recursive sequences. Then find the 5th and 10th terms of each sequence.
A. a1= 12; an = an-1 - 7
B. a1= 5; an = an-1 + 25
A. an = 12 + (n-1)* (-7)
a5 = -16
a10 = -51
B. an = 5 + (n-1) * 25
a5 =105
a10 = 230
Create a linear regression on Desmos given the following data. Then determine the equation of the line of best fit, the strength and direction of the relationship, and predict the y-value when x = 25
x = 2,3,5,7,11,9,15
y = 4,8,10,11,15,16,22
Equation: f(x) = 1.26174x + 2.91275
Strong Positive Relationship
f(25) = 34.45625