Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

The point P(3, 8) is on the graph of y = b^x, where b > The corresponding point, P′, on the graph of y + 3 = b^(x + 1) is?

4 Answers

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  • 2 months ago
    Favorite Answer

    y = bˣ

    y + 3 = b⁽ ˣ ⁺ ¹ ⁾

    y = b⁽ ˣ ⁺ ¹ ⁾ - 3

    In other words to get to y = b⁽ ˣ ⁺ ¹ ⁾ - 3 the original y = bˣ is translated 1 unit to the left and vertically shifted 3 units down.

    Corresponding point:

    x = 3 - 1 = 2

    y = 8 - 3 = 5

    P’( 2, 5 )

    ━━━━

  • ted s
    Lv 7
    2 months ago

    ( 7 , 0 ) under the given transformation

  • Pope
    Lv 7
    2 months ago

    This concept is usually presented as a function transformation, but it actually is a translation that can apply to any graph in the x-y plane.

    Let x be replaced by (x - a).

    Let y be replaced by (y - b).

    The result is a translation by vector <a, b>.

    y = b^x

    y + 3 = b^(x + 1)

    y - (-3) = b^[x - (-1)]

    In this case, a = -1 and b = -3.

    Translate point P(3, 8) by vector <-1, -3>.

    P(3, 8) → P'(2, 5)

  • 8 = b^3

    y + 3 = b^(3 + 1)

    y + 3 = b^(4)

    y + 3 = (b^3)^(4/3)

    y + 3 = (8)^(4/3)

    y + 3 = 2^4

    y + 3 = 16

    y = 13

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