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?

Relevance
• 2 months ago

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 )

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• 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)

• 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