$100 $200 $300 $400 $500 $200 $300 $400 $500 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 DomainRange 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 = ( )/ (0-1) m = -2/-1 = 2 y = mx + b y = 2x +b -3 = 2(0) + b b = -3 y = 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 = 5y 5y = -x y = (-1/5)x k = (-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 = kx y/x = k 24/6 = k 4 = k y = 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. XY

Answer It is Inverse Variation. k = 24 Back XYy/xxy /

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

Answer Yes, x(y – 1) = -x + 3 xy – x = -x + 3 xy – x + x = -x + x +3 xy = 3 y = 3/x Thus, 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/x yx = k 3*4 = k 12 = k y = 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/x yx = k 2*1 = k 2 = k y = 2/x Back

Inverse Variation for $500 Is the following table inverse, direct, or neither? Find k. XY

Answer It is direct variation, k = 8 Back XYy/xxy

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) = a 1 + (n-1)d Where: n is the nth term a 1 is the first term d is the common difference Back

Number Patterns for $300 Find the 7 th 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 3127 th term in the following arithmetic sequence: 13, 10, 7, 4, …

Answer Back A(n) = a1 + (n-1)d A(3127) = 13 + (3127 – 1) * -3 A(3127) = * -3 A(3127) = A(3127) = -9365