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Math Help - Graphing Techniques

  1. #1
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    Graphing Techniques

    Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of y = x^2 and show all stages.

    Before showing me how to graph the functions below, I need a clear definition of the words:

    *shifting
    *compressing
    *stretching
    *reflecting

    What do the words above mean in math?

    QUESTIONS:

    (1) f(x) = sqrt{x + 1}

    (2) f(x) = h(x) = 2int(x - 1)
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  2. #2
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    Quote Originally Posted by symmetry View Post
    Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of y = x^2 and show all stages.

    Before showing me how to graph the functions below, I need a clear definition of the words:

    *shifting
    *compressing
    *stretching
    *reflecting

    What do the words above mean in math?

    QUESTIONS:

    (1) f(x) = sqrt{x + 1}

    (2) f(x) = h(x) = 2int(x - 1)
    compressing/stretching; f(x) = c*g(x), where c is a constant; if this constant is greater than one, then the graph has been vertically stretched. If it is between 0 and 1, then the graph has been vertically compressed.

    Now, HORIZONTALLY stretching/compressing occurs when the x values have been multiplied by a constant. That is, f(x) = g(cx); if this constant is greater than one, then the graph has been horizontally compressed. If it is between 0 and 1 then the graph has been horizontally stretched.

    Graphs of a function f(x) are said to be reflected (across the y-axis) when the x values of the function have been multiplied by a negative value. And, the graph is said to be reflected (across the x-axis) when the y values of the function have been multiplied by a negative value.

    Some notes:

    y = f(x) + 10 shifts the graph up 10 units- this affects the y values.

    Similarly, y = f(x) - 10 shifts the graph down 10 units.

    For example: g(x) = x^2 + 10

    A vertical stretch with a factor of 5 is: y = 5*f(x); this multiplies the y values by the constant, 5.

    For example: g(x) = 3*sqrt(x)

    Vertical compression by a factor of 10: y = 1/10*f(x); this multiplies the y-values by 1/10.

    A vertical reflection about the x-axis: y = -f(x)

    Horizontal shifts, compressions, etc affect the x values.

    A graph shifted 10 units horizontally to the left, a graph shifted 10 units horizontally to the right, a graph stretched horizontally by a factor of 1/10, and a graph compressed by a factor of 5 are all given, respectively, below:

    y = f(x + 10)

    y = f(x - 10)

    y = f((1/10)x)

    y = f(5x)

    And finally, a horizontal reflection about the y-axis is given by:

    y = f(-x)

    (Which multiplies the x-values by -1).
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  3. #3
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    Quote Originally Posted by symmetry View Post
    QUESTIONS:

    (1) f(x) = sqrt{x + 1}

    (2) f(x) = h(x) = 2int(x - 1)
    You should be able to do these now after my explanation; the first shifts the graph to the left 1 unit; the second stretches the graph vertically by a scalar of 2 and shifts it right by 1.
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  4. #4
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    ok

    I follow everything you said except the math phrase:

    "scalar".

    What is a scalar?

    You said, "scalar of 2."

    What do you mean by this statement?

    Yes, I can graph the functions using your steps.

    Scalar?????
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  5. #5
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    Quote Originally Posted by symmetry View Post
    I follow everything you said except the math phrase:

    "scalar".

    What is a scalar?

    You said, "scalar of 2."

    What do you mean by this statement?

    Yes, I can graph the functions using your steps.

    Scalar?????
    A scalar is a (real) number used to multiply the function; think of it as constant multiplied to stretch the graph, compress it, etc.
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  6. #6
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    ok

    Thanks for the definition of scalar.
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