Question

describe the transformation from the parent function $f(x)=\sqrt{x}$ $f(x)=3\sqrt{x - 7}+4$ vertically stretched by a factor of 3 shifted down by 7 units shifted right by 4 units reflects does not reflect

Explanation:

Step1: Analyze vertical stretch

The coefficient \(3\) in front of \(\sqrt{x - 7}\) means the graph is vertically stretched by a factor of \(3\) (since \(a>1\) in \(a\sqrt{x - h}+k\) causes vertical stretch).

Step2: Analyze horizontal shift

The \(-7\) inside the square root: for \(f(x)=\sqrt{x - h}\), \(h = 7\) means a shift right by \(7\) units (not \(4\)).

Step3: Analyze vertical shift

The \(+4\) at the end: for \(f(x)=\sqrt{x - h}+k\), \(k = 4\) means a shift up by \(4\) units (not down by \(7\)).

Step4: Analyze reflection

There's no negative sign, so it does not reflect.

Correct transformations: Vertically stretched by a factor of \(3\), shifted right by \(7\) units, shifted up by \(4\) units, does not reflect.

Answer:

• Vertical transformation: Vertically stretched by a factor of \(3\) (correct as is).
• Horizontal shift: Shifted right by \(7\) units (not \(4\)).
• Vertical shift: Shifted up by \(4\) units (not down by \(7\)).
• Reflection: Does not reflect (correct as is).