Question

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\\(y = x^3\\)
\\(y = |x|\\)
\\(y = \sqrt{x}\\)
\\(y = \sqrt3{x}\\)

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

c) choose the correct transformation (stretches/compressions).
vertical compression by a factor of 3/4

d) choose the correct transformation (vertical shifts).
select an answer

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

Explanation:

Step1: Identify the parent function

$$y = \sqrt{x}$$

Step2: Identify the transformed function

$$y = \frac{3}{4}\sqrt{x}$$

Step3: Determine the vertical shift

$$\text{No constant is added to the function, so there is no vertical shift.}$$

Step4: Determine the horizontal shift

$$\text{No constant is added to the input variable } x \text{, so there is no horizontal shift.}$$

Answer:

d) No vertical shift
e) No horizontal shift