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Transcript of $100 $200 $300 $400 $500 $200 $300 $400 $500 Graphing Events/ Relations Function rules, tables, and...
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Graphing Events/ Relations
Function rules, tables, and graphs
Number Patterns
Direct Variation
Inverse Variation
Graphing Events/ Relations for $100
Define: Relation
Answer
Back
Relation – A set of ordered pairs
Graphing Events/ Relations for $200
What is wrong with the graph shown below:
Answer
Back
Distance can never go down, only displacement can.
Graphing Events/ Relations for $300
Write a description of the following graph:
Answer
Back
The cost of gasoline over time
Graphing Events/ Relations for $400
Draw a graph to represent the amount of money I have if I am paying a mechanic $100/hour to fix my car
Answer
Back
Graphing Events/ Relations for $500
Draw a time vs speed graph that shows a person standing still
Answer
Back
Time
Speed
Function Rules, Tables and Graphs for $100
Draw a mapping diagram for the following set of data. Is it a function?
(3,4)(2,1)(5,7)(3, -2)
Answer
Back
235
Domain Range
-2147
No it is not a function because one input (3) goes to two outputs (4 and -2)
Function Rules, Tables and Graphs for $200
Write the following equation in function notation:
y = 3x - 4
Answer
y = 3x - 4
f(x) = 3x-4
Back
Function Rules, Tables and Graphs for $300
Graph the following function rule:
f(x) = |x| -2
Answer
f(x) = |x| - 2
Back
Function Rules, Tables and Graphs for $400
Use the vertical line test to determine if the following graph is a function
Answer
Back
Yes, it is a function because the vertical line never hits more than one point at a time.
Function Rules, Tables and Graphs for $500
Write the function rule from the given graph.
Answer
Back
Two points on the graph: (0, -3) and (1, -1)m = (y2 – y1)/(x2 – x1)m = (-3 - -1)/ (0-1)m = -2/-1 = 2y = mx + by = 2x +b-3 = 2(0) + bb = -3y = 2x - 3
Direct Variation for $100
Write the equation for direct variation.
Answer
Direct Variation:
y = kx; k≠0
Back
Direct Variation for $200
Is the following equation direct variation? If it is, solve for the constant of variation.
-x = 5y
Answer
Yes, because:-x = 5y5y = -xy = (-1/5)xk = (-1/5)
Back
Direct Variation for $300
Write an equation of the direct variation that includes the given point:
(6, 24)
Answer
(6, 24)Direct Variation: y = kxy/x = k24/6 = k4 = ky = 4x
Back
Direct Variation for $400
Graph the direct variation that includes the given point:
(3, 6)
Answer(3, 6)
Direct Variation: y = kx
y/x = k
6/3 = k
2 = k
y = 2x
Back
Direct Variation for $500
Is the following table inverse, direct, or neither? Find k.
X Y
1 24
2 12
3 8
4 6
Answer
It is Inverse Variation. k = 24
Back
X Y y/x xy
1 24 24 24
2 12 6 24
3 8 8/3 24
4 6 1.5 24
Inverse Variation for $100
Write the equation for inverse variation.
Answer
y = k/x; x ≠0, k≠0
Back
Inverse Variation for $200
Is the following equation inverse variation? If it is, solve for the constant of variation.
x(y – 1) = -x + 3
AnswerYes,x(y – 1) = -x + 3xy – x = -x + 3xy – x + x = -x + x +3xy = 3y = 3/xThus, k = 3
Back
Inverse Variation for $300
Write an equation of the inverse variation that includes the given point:
(3, 4)
Answer
(3, 4)Inverse Variation: y = k/xyx = k3*4 = k12 = ky = 12/x
Back
Inverse Variation for $400
Graph the inverse variation that includes the given point:
(1, 2)
Answer(1, 2)Inverse Variation: y = k/xyx = k2*1 = k2 = ky = 2/x
Back
Inverse Variation for $500
Is the following table inverse, direct, or neither? Find k.
X Y
1 8
2 16
3 24
4 32
Answer
It is direct variation, k = 8
Back
X Y y/x xy
1 8 8 8
2 16 8 32
3 24 8 72
4 32 8 128
Number Patterns for $100
Define: Arithmetic Sequence
Answer
Arithmetic Sequence – A number pattern formed by adding a fixed number to each previous term
Back
Number Patterns for $200
What is the formula for finding the nth term of an arithmetic sequence?
Answer
A(n) = a1 + (n-1)d
Where:
n is the nth term
a1 is the first term
d is the common difference
Back
Number Patterns for $300
Find the 7th term of the following sequence:
3, 9, 27, 81, …
Answer
The rule is multiply by 3 so,
3, 9, 27, 81, 243, 729, 2187
Back
Number Patterns for $400
Define: Inductive reasoning
Answer
Inductive Reasoning – Making conjectures (conclusions) based on examples and patterns
Back
Number Patterns for $500
Find the 3127th term in the following arithmetic sequence:
13, 10, 7, 4, …
Answer
Back
A(n) = a1 + (n-1)dA(3127) = 13 + (3127 – 1) * -3A(3127) = 13 + 3126* -3A(3127) = 13 + -9378A(3127) = -9365
