Question

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Answer 1

Answer: D) reflection over the x-axis, vertical shrink by a factor of 7/8, horizontal shift 3 units to the left, and vertical shift 3 units up.

Explanation:

`Consider\ f(x)=Ae^(Bx-C)+D\qquad where`

• A = vertical stretch by a factor of A (|A| < 1 is a vertical shrink)
• -A = reflection across the x-axis
• B = horizontal shrink by a factor of 1/B
• C = horizontal shift C units (positive = right, negative = left)
• D = vertical shift D units (positive = up,, negative = down)

`f(x)=e^x\\\\g(x)=-(7)/(8)e^(x+3)+3`

→ A = -(7/8)

The negative sign represents a reflection across the x-axis.

(7/8) < 1 so it is a vertical shrink by a factor of (7/8)

→ C = -3 x +3 = x - (-3)

This is a horizontal shift 3 units to the left.

→ D = +3

This is a vertical shift 3 units up.