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    Basic Algebra - Relations and functions

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    #28: y=-2x2+3

    x y=-2x2+3 y
    0 y=-2(0)2+3 3
    1 y=-2(1)2+3 1
    2 y=-2(2)2+3 -5
    -1 y=-2(-1)2+3 1
    -2 y=-2(-2)2+3 -5

    • The graph of the relation is  (x)=-2x2+3.

    • My 5 points for this equation is as follows:
    (0,3)
    (1,1)
    (2,-5)
    (-1,1)
    (-2,-5)

    • The key points and general shape of this graph is upward and the vertex is 3 located on the y-intercept. This is a parabola.

    • The domain is (-,).

    • The range is (-, 3].

    • This graph is a function because each y value equals one x value. "If the value of the variable y is determined by the value of the variable x, then y is a function of x. So is a function of means is uniquely determined by" (Dugopolski, 2012, p. 690).

    • The vertical line test passes through any x value and it only crosses that line once.

    #36: y=2(x)+1
    x y=2(x)+1 y
    0 y=2(0)+1 1
    1 y=2(1)+1 3
    2 y=2(2)+1 3.82
    4 y=2(4)+1 5
    6 y=2(6)+1 5.89
    • The graph of the relation is  (x)=2(x)+1.

    • My 5 points for this equation is as follows:
    (0,1)
    (1,3)
    (2,3.82)
    (4,5)
    (6,5.89)

    • This graph is a function because each y value equals one x value.

    • The general shape of this graph is a curve that plateau. There is no vertex.

    • I selected problem 36 to be shifted 3 units upward and 4 units to the left.
    y=2(x)+1
    y=2(x+4)+1+3
    y=2(x+4)+4

    • This is the transformation of the function. I added 3 outside the radical and added 4 inside the radical.

    Page 709 #28
    This problem is an example of a quadratic function. We know this because it is in the form f(x)=ax2+bx+c where a, b, and c are real numbers and a is not equal to 0. In this case, we will graph the given function by plotting enouh points to figure out the shape of the graph.

    Y = -2x2+3 original equation.
    X Y In this portion, I just plugged in the values under the x column
    -2 -5 into the equation above and found the corresponding solutions
    -1 1 for y. These are the ordered pairs that will appear on the
    0 3 graph.
    1 1
    2 -5
    This is a function because each value for y only has one x value and passes a vertical line test. The vertex for this parabola is [0,3], the domain is {[-∞, ∞]}, and the range is {[-∞,3]}.

    Page 709 #36
    This problem is a square root function because it comes in the form f(x)= √x.

    Y = 2√(x)+1 original equation.
    X Y In this portion, I just plugged in the values under the x column
    0 1 into the equation above and found the corresponding solutions
    1 3 for y. These are the ordered pairs that will appear on the graph.
    4 5
    9 7
    This is a function because each value for y only has one x value and passes a vertical line test. The domain for this graph is {[0, ∞]} and the range is [{1, ∞}].
    Had this line been shifted up three and left four a transformation in the graph and equation would occur. (x)+ c represents a line shifting up c units and (x+c) represents a line shifting left c units. The change to the equation is shown below.
    Y= 2√(x )+1
    Y= 2√(x+4) +1+3
    Y= 2√(x+4) +4

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    https://brainmass.com/math/basic-algebra/basic-algebra-relations-functions-578680

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    Solution Preview

    Relations and Functions
    #28: y=-2x2+3

    x y=-2x2+3 y
    0 y=-2(0)2+3 3
    1 y=-2(1)2+3 1
    2 y=-2(2)2+3 -5
    -1 y=-2(-1)2+3 1
    -2 y=-2(-2)2+3 -5

    • The graph of the relation is  (x)=-2x2+3.

    • My 5 points for this equation is as follows:
    (0,3)
    (1,1)
    (2,-5)
    (-1,1)
    (-2,-5)

    • The key points and general shape of this graph is an downward parabola and the vertex is at x=3 located on the y-intercept. The point of the vertex is (0,3)

    • The domain is (-,).

    • The range is (-,3].

    • This graph is a function because each y value equals one x value. "If the value of the variable y is determined by the value of the variable x, then y is a function of x. So is a function of means is uniquely determined by" ...

    Solution Summary

    Relations and functions for basic algebra are provided.

    $2.19