Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 42 views

    3.3 Linear Functions

    Uploaded by

    m_armouti
    1) The document discusses linear functions and how to identify, write, and graph them. It defines key terms like x-intercept and y-intercept. It shows how to write a linear equation in standard form and determine if equations are linear. Examples are provided to demonstrate identifying linear equations and finding intercepts and zeros of linear functions. 2) The document provides steps for graphing linear equations by making a table of x- and y-values and plotting points. Examples demonstrate these graphing steps. Review questions assess understanding of key graphing concepts like intercepts, slope, and domain. 3) Additional practice problems are provided for students to work on identifying linear equations

    Copyright:

    © All Rights Reserved
    Download as PPT, PDF, TXT or read online from Scribd

    3.3 Linear Functions

    Uploaded by

    m_armouti
    42 views28 pages
    1) The document discusses linear functions and how to identify, write, and graph them. It defines key terms like x-intercept and y-intercept. It shows how to write a linear equation in standard form and determine if equations are linear. Examples are provided to demonstrate identifying linear equations and finding intercepts and zeros of linear functions. 2) The document provides steps for graphing linear equations by making a table of x- and y-values and plotting points. Examples demonstrate these graphing steps. Review questions assess understanding of key graphing concepts like intercepts, slope, and domain. 3) Additional practice problems are provided for students to work on identifying linear equations

    Original Description:

    Copyright

    © © All Rights Reserved

    Available Formats

    PPT, PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    1) The document discusses linear functions and how to identify, write, and graph them. It defines key terms like x-intercept and y-intercept. It shows how to write a linear equation in standard form and determine if equations are linear. Examples are provided to demonstrate identifying linear equations and finding intercepts and zeros of linear functions. 2) The document provides steps for graphing linear equations by making a table of x- and y-values and plotting points. Examples demonstrate these graphing steps. Review questions assess understanding of key graphing concepts like intercepts, slope, and domain. 3) Additional practice problems are provided for students to work on identifying linear equations

    Copyright:

    © All Rights Reserved
    Download as PPT, PDF, TXT or read online from Scribd
    Download as ppt, pdf, or txt
    42 views28 pages

    3.3 Linear Functions

    Uploaded by

    m_armouti
    1) The document discusses linear functions and how to identify, write, and graph them. It defines key terms like x-intercept and y-intercept. It shows how to write a linear equation in standard form and determine if equations are linear. Examples are provided to demonstrate identifying linear equations and finding intercepts and zeros of linear functions. 2) The document provides steps for graphing linear equations by making a table of x- and y-values and plotting points. Examples demonstrate these graphing steps. Review questions assess understanding of key graphing concepts like intercepts, slope, and domain. 3) Additional practice problems are provided for students to work on identifying linear equations

    Copyright:

    © All Rights Reserved
    Download as PPT, PDF, TXT or read online from Scribd
    Download as ppt, pdf, or txt
    of 28

    Given g(x) = 2x2 +1 , find g(3)

    g(3)=2(3)2 +1
    g(3)=2(9)+1
    g(3)=19
    Given f(x) = 3x - 1, find 4[f(4) – f(2)]
    Given h(x) = 5+5x, find [f(4) – f(1)](-2)
    3.3 Linear Functions
    The student will be able to:
    1. identify linear functions.
    2. write equations in standard form.
    3. Graph linear functions.

    Indicators:
    Designed by Skip Tyler, Varina High School
    Vocabularies
    • A linear equation is the equation of a line.
    • An x-intercept is a point on the graph where y is
    zero. In other words, an x-intercept is a point in the
    equation where the y-value is zero.
    • A y-intercept is a point on the graph where x is
    zero. In other words, a y-intercept is a point in the
    equation where the x-value is zero.
    • Values of x for which f(x)=0 are called zeros. For a
    linear function, the zero is its x-intercept.
    Standard Form
    Ax + By = C
    A, B, and C have to be integers
    An equation is LINEAR (the graph is
    a straight line) if it can be written in
    standard form.
    This form is useful for graphing
    (later on…).
    Determine whether each equation is
    a linear equation.
    1) 4x = 7 + 2y
    Can you write this in the form
    Ax + By = C?
    4x - 2y = 7
    A = 4, B = -2, C = 7
    This is linear!
    Determine whether each equation is
    a linear equation.
    2) 2x2 - y = 7
    Can you write it in standard form?
    NO - it has an exponent!
    Not linear
    3) x = 12
    x + 0y = 12
    A = 1, B = 0, C = 12
    Linear
    Here’s the cheat sheet! An equation that is
    linear does NOT contain the following:
    1. Variables in the denominator
    3
    y  2
    x
    2. Variables with exponents
    y  x 3
    2

    3. Variables multiplied with other


    variables.
    xy = 12
    Is this equation linear?
    x  4y  3
    1. Yes
    2. No

    Standard Form
    x – 4y = 3
    Is this equation linear?
    9  4y  x
    2

    1. Yes
    2. No

    Exponents are
    not allowed!
    Is this equation linear?
    y = -3

    1. Yes
    2. No

    Standard Form
    0x + y = -3
    Review of the definition.

    • An x-intercept is a point on the graph where y is zero. In


    other words, an x-intercept is a point in the equation where the
    y-value is zero.
    • A y-intercept is a point on the graph where x is zero. In other
    words, a y-intercept is a point in the equation where the x-
    value is zero.
    • Values of x for which f(x)=0 are called zeros. For a linear
    function, the zero is its x-intercept.
    Determine the x-intercept, y-intercept,
    and zero of the linear equation y=10x-1.
    x-intercept: y-intercept:
    •Set y=0 •Set x=0
    •Solve for x •Solve for y
    0=10x-1 y=10(0)-1
    +1 +1
    1=10x y=-1
    x=1/10
    Determine the x-intercept, y-intercept,
    and zero of the linear equation
    y=10x-1.
    x-intercept: y-intercept:
    Find the x-intercept, y-intercept,
    and zero for the graph of the line.
    Solution:
    The x-intercept of this graph is 4.
    The coordinates of the point at the
    x-intercept is (4, 0).
    The y-intercept of this graph is 2.
    The coordinates of the point at the
    y-intercept is (0, 2).
    Find the x-intercept, y-intercept,
    and zero for the graph of the line.
    x-intercept: -3
    y-intercept: 3
    zero: 3
    Work on the following problems:
    • P 158 #3, 12-19 all,
    Graph an equation by making a
    table
    Graphing Steps
    1) Isolate the variable (solve for y).
    2) Make a t-table. If the domain is
    not given, pick your own values.
    3) Plot the points on a graph.
    4) Connect the points.
    1) Review: Solve for y
    2x + y = 4
    1. Draw “the river”
    - 2x - 2x
    2. Subtract 2x from
    both sides
    y = -2x + 4
    2) Solve for y: 4x + 2y = -6
    1. Subtract 4x - 4x - 4x
    2. Simplify 2y = -4x - 6
    3. Divide both sides by 2 2 2
    4. Simplify y = -2x - 3
    3) Solve for y: x - 3y = 6
    1. Subtract x - x - x
    2. Simplify -3y = -x + 6
    3. Divide both sides by -3
    -3 -3
    4. Simplify
    x  6
    y
    3
    or x
    y  2
    3
    4) Review: Make a t-table
    If f(x) = 2x + 4, complete a table
    using the domain {-2, -1, 0, 1, 2}.
    x f(x) ordered pair
    -2 2(-2) + 4 = 0 (-2, 0)
    -1 2(-1) + 4 = 2 (-1, 2)
    0 2(0) + 4 = 4 (0, 4)
    1 2(1) + 4 = 6 (1, 6)
    2 2(2) + 4 = 8 (2, 8)
    5) Given the domain {-2, -1, 0, 1, 2},

    graph 3x + y = 6
    1. Solve for y: 3x + y = 6
    Subtract 3x - 3x - 3x
    2. Make a table
    x -3x + 6 y = -3x + 6
    ordered pair
    -2 -3(-2) + 6 = 12 (-2, 12)
    -1 -3(-1) + 6 = 9 (-1, 9)
    0 -3(0) + 6 = 6 (0, 6)
    1 -3(1) + 6 = 3 (1, 3)
    2 -3(2) + 6 = 0 (2, 0)
    5) Given the domain {-2, -1, 0, 1, 2},

    3.
    graph 3x
    Plot the points
    + y = 6
    (-2,12), (-1,9), (0,6), (1,3),
    (2,0)
    4. Connect the points.
    Bonus questions!
    What is the x-intercept?
    (2, 0)
    What is the y-intercept?
    (0, 6)
    Does the line increase or decrease?
    Decrease
    5) Given the domain {-2, -1, 0, 1, 2},

    graph 4x + 2y = 6
    Which is the graph of y = x – 4?
    1. .
    2. .
    3. .
    4. .
    • P 158 36-37, 39-43 odds ( might change
    due to time consuming)

    You might also like