Arithmetic Sequences
Key Features of Linear Functions
Linear vs. Non-Linear
Applications
X & Y Intercepts
Domain & Range
100
Is the sequence arithmetic? If yes, find the common difference.
−30, −40, −50, −60, ...
Yes, d=-10
100
Determine the domain & range of the graph.
D: All real numbers
R: All real numbers
100
Which graph represents a linear function?
D
100
Carter is opening a savings account. Initially, he deposits $300 and adds $50 each month. Write an equations to represent the amount he has saved each month.
S = 300 + 50m
100
What is the y-intercept of the equation below:
y = -10 + 40x
y = -10
100
Is domain input value, x or output value, y?
x
200
an = −7.1 − 2.1n
Find a27
a27=-63.8
200
Determine the domain & range.
D: [0, 12]
R: [300, 1500]
200
Is this graph a linear function? Why or why not?
No, it does not have a constant rate of change.
200
Madi is selling charm bracelets. The bracelets are sold at a flat rate of $10 plus $2 per charm. Write an explicit equation to represent the total cost of a charm bracelet.
an = 12 + 2(n-1)
200
What is the x-intercept of the equation below:
y = -10 + 40x
x = 0.25 or 1/4
200
Identify the range of the function.
300
Find the common difference:
a2 = 34, a4 = -4
d=-19
300
Name both intercepts.
x = -4
y = 2
300
Which of the following equations is a non-linear function?
A. y = 4
B. y = x2 - 4
C. m = 1.3r - 1000
D. x = 3
B
300
Write a linear equation for the following graph.
y = -2x + 140
300
Determine the x&y intercepts
x = 4
y = 5
300
What is the domain of the function?
400
Write the explicit formula:
a1 = −26, d = 200
an = -26 + 200(n-1)
400
Determine the rate of change.
-2 degrees/hour
400
Non-linear
400
What does the x-intercept represent in the context of the scenario?
After 8 seconds, you will be on the ground floor.
400
Determine the x & y intercept of the equation below:
3x - 4y = 12
y = -3
x = 4
400
Ms. Chang sells homemade lemonades. She makes 10 lemonades after school every day. Each lemonade requires 3 lemons. The number of lemons she uses depends on the total number of lemonades made. She makes at least one lemonade a day. Define and write your domain and range.
D: Number of lemonades
{x│x= 1, 2, 3, 4… 10}
R: Number of lemons
{y│y= 3, 6, 9, 12…30}
500
Write the explicit formula:
a38 = −53.2, d = −1.1
an = -12.5 -1.1(n-1)
500
Determine f(125)
f(125) = 10
500
Is the table linear or non-linear? If so, what is the rate of change?
Yes, -5/3
500
A landscaping company charges a flat fee of $25 for a consultation, plus $1.50 for every square foot of lawn they treat.
A) Write a function that would represent the total cost(C) to service a lawn, given the size of the lawn in square feet (s).
B) How much will it cost to treat a lawn that is 400 square feet?
C = 1.5s + 25
C = $625
500
Determine the x & y intercept of the equation below:
-4x - 6y = 36
x = -9
y = -6
500
Which situation could be modeled by a function with a domain that includes both positive and negative real numbers?
A. The height of skydiver after deploying as a function of time flying
B. A baby’s weight as a function of time since birth
C. A car tire’s pressure as a function of temperature
D. The time required to play a golf game as a function of the number of holes played
C