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.
Step-by-step explanation:
[tex]Consider\ f(x)=Ae^{Bx-C}+D\qquad where[/tex]
- 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)
[tex]f(x)=e^x\\\\g(x)=-\dfrac{7}{8}e^{x+3}+3[/tex]
→ 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.
