Graphing Relationships & Functional Notation
Linear Functions/Slope
Identify/Graph Sequences
Arithmetic Sequences
100
Is the following graph a function? If no, explain.
No, it fails the vertical line test.
100
Find the slope between the following points:
(-4,5) & (0, 17)
m = 3
100
The graph represents the speed of a bicycle going down a hill. Identify the independent and dependent variables.
Independent: Time (seconds)
Dependent: Speed (mph)
100
Identify the following about the given sequence:
3, -6, 12, -24, 48
a) Is the sequence arithmetic or non-arithmetic? Justify your answer with work like your notes.
b) What are the next 2 terms? Provide regardless of your answer in part 'a' and show your work.
a) Non-arithmetic. The sequence goes from 3 to -6, which is a difference of -9. From -6 to 12 the difference is 18. There is NO common difference.
b) The pattern is multiplied by -2. -2(48) = -96 and -2(-96) = 192. The next two terms are -96 and 192.
200
Is the following mapping a function? Why or why not?
Yes, every input has only one output.
200
Find the slope between the following points:
(6,-1) & (6, 5)
m= Undefined
200
Determine the type of each domain as continuous or discrete.
a) A plane taking off and reaching a cruising altitude.
b) The amount of shots I make playing a round of golf.
a) Continuous
b) Discrete
200
Find the simplified explicit rule for the given sequence.
an = 12n + 8
300
The following graph represents the path of football being thrown. What is the height of the football at 3 seconds and describe what is happening at this point in time.
The height of the football is 8 ft and the football got deflected off the receiver or defense player, which is why it went back into the air after t = 3 seconds.
300
Bobby has sold $81 worth of candy bars so far. He has more candy bars is selling them for $3 a piece. Write a function using functional notation that represents the total sales. Use 'c' for the number of candy bars.
f(c) = 81 + 3c
300
Find the 7th term for the following explicit formula.
f(n) = -4(n-1) + 9
f(7) = -15
300
Find the term position that has the given value for the explicit formula provided. an = -3n + 8; an = -31
n = 13
400
Find the following:
a) f(6)
b) x when f(x) = 12
c) Range
a) f(6) = 15
b) x = 1 and x = 3.5
c) 0≤y≤20
400
Find the range for the given function and domain.
Domain: {-9, -3, 0, 12, 21}
f(x) = 1/3x-4
Range: {-7, -5, -4, 0, 3}
400
Find the following based on the graph.
a7 =
For an = 3, n =
f(3) =
a7 = 5
For an = 3, n = 9
f(3) = 4
400
For the given sequence, write both the Recursive and simplified Explicit formulas: -5, -8, -11, -14 . . . .
Recursive: f(n) = f(n-1) - 3; f(1) = -5
Explicit: an = -3n - 2
500
Find f(8) if f(x) = -3x2 + 5
f(8) = -187
500
Find the 'y' value that makes the slope of the line between the given points equal to the given slope.
(-4,y) & (2,-7); m = 5
y = -37
500
Find the 5th term for the given recursive sequence.
f(1) = 2; f(n) = 3f(n-1) + 6
f(5) = 402
500
Given two terms in an arithmetic sequence, write the simplified explicit rule: a10=12 and a15=37
an = 5n - 38