Question

y = 2√x - 5; what are the transformations for the graph of the parent function f(x) = √x to the function above; options: vertical stretch by a factor of 2; translated down 5 units; shifted right 2 units and down 5 units; vertical stretch by a factor of 2; translated left 5 units; vertical stretch by a factor of 2; translated right one unit

Explanation:

Step1: Analyze Vertical Stretch

For a function \( y = a\sqrt{x} \), the \( a \) value determines vertical stretch/compression. Here \( a = 2 \), so vertical stretch by factor 2.

Step2: Analyze Vertical Translation

For a function \( y = \sqrt{x}+k \), \( k \) determines vertical shift (up if \( k>0 \), down if \( k<0 \)). Here \( k=-5 \), so translated down 5 units.

Step3: Analyze Horizontal Translation

There's no horizontal shift (no \( (x - h) \) form with \( h
eq0 \)), so no horizontal shift.

Answer:

A. Vertical Stretch by a factor of 2; translated down 5 units