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# 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?

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- King LeoLv 72 months agoFavorite 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 )

━━━━

- PopeLv 72 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)

- 2 months ago
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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