Question

b) choose the correct transformation (reflections).
no reflections

c) choose the correct transformation (stretches/compressions).
vertical stretch by a factor of 3

d) choose the correct transformation (vertical shifts).
vertical shift down 5 units

e) choose the correct transformation (horizontal shifts).
select an answer

Explanation:

Step1: Identify the base function and transformations

$$y = a \cdot f(b(x - h)) + k$$

Step2: Analyze the given transformations

$$a = 3 \implies \text{Vertical stretch by a factor of 3}$$

$$k = -5 \implies \text{Vertical shift down 5 units}$$

$$\text{No reflections} \implies a > 0, b > 0$$

Step3: Determine the horizontal shift

$$h = 0 \implies \text{No horizontal shift}$$

Answer:

No horizontal shift