Chapter Review

Chapter 3A Review Notes

Page 1

• Function Relations

  • Can arrows be drawn from 10.3 to make the relation a function?

    • Explanation: A relation is a function if each input has exactly one output. Analyze the given diagram for multiple outputs.

• Function from a Table

  • Input/Output table:

    • Input: 2, 4, 6, 8, 10

    • Output: 1, 2, 3, 4, 3

    • Function Check: Assess whether each input yields a unique output.

• Rate of Change

  • Compare two linear functions based on the given equations.

    • Function A: (Details needed)

    • Function B: y = 11x - 1

    • Greater Rate of Change: Analyze slopes to justify.

• Study Time and Grades

  • Relation Analysis: Neil's study hours vs. grades

    • Input (Hours): 4, 6, 6

    • Output (Grades): 75, 75, 82

    • Use a graph to justify whether the relation represents a function.

• Linear vs. Nonlinear Function

  • Determine if a given function is linear based on the definition: a function that graphs to a straight line (constant rate of change).

• Function Check with a Set of Points

  • Points: (-5, -3), (7, 2), (3, 8), (3, -8), (5, 10)

  • Function Determination: Use an arrow diagram to check if each x-value has one y-value.

• Gift Card Equation

  • Mark's Gift Card:

    • Initial Amount = $100, Cost per App = $4.99

    • Equation: y = 100 - 4.99x where y is the amount left and x is the time in weeks.

  • Graph: Plot the function based on the equation.

• Graph Description

  • What best describes the graph?

    • Options: Relation only, Function only, both.

    • Analyze points and whether each input corresponds to a single output.

Page 2

• Function Identification

  • Representations:

    • A, B, C, D (examine structures for unique outputs).

• Rate of Change Comparison

  • Two items with sets of x and y values (identified as I and II).

    • Analysis of the slope from the data points.

• Rates and Intercepts

  • Function A: y = -3x + 2

  • Function B: (cited in another example)

  • Compare initial values and rates of change visually or with calculations.

• Fencing Price Table

  • Table displayed:

    • Length (feet): 75, 125, 175, 225

    • Price: $168.75, $281.25, $393.75, $506.25

    • Compare store prices:

      • Bargain: y = 2.50x

      • Calculate unit price for each.

• Graphing a Linear Equation

  • Given equation to graph: -6x + 3y = -9

    • Step-by-step instructions for graphing.

Page 3

• Rate of Change for Functions

  • Function A and Function B rate of change analysis needed.

    • Provide numerical and graphical analysis of slopes.

  • Fill in the boxes:

    • Function A - Rate of Change

    • Function B - Rate of Change

    • Calculate the comparative rate of change between A and B.