Test Questions for Graphing Square Root Function Transformations

📚 Quick Study Guide

• 🔍 The parent square root function is $f(x) = \sqrt{x}$.
• 📈 Transformations involve shifts, stretches, compressions, and reflections.
• ➡️ Horizontal shifts: $f(x-h)$, where $h>0$ shifts right and $h<0$ shifts left.
• ⬆️ Vertical shifts: $f(x) + k$, where $k>0$ shifts up and $k<0$ shifts down.
• растяжение Vertical stretch/compression: $a f(x)$, where $|a|>1$ stretches and $0<|a|<1$ compresses.
• отражение Reflection over the x-axis: $-f(x)$.
• ⬅️ Horizontal stretch/compression: $f(bx)$, where $|b|>1$ compresses and $0<|b|<1$ stretches.
• 🔄 Reflection over the y-axis: $f(-x)$.
• 📝 General form: $a\sqrt{b(x-h)} + k$

🧪 Practice Quiz

1. What transformation does the function $f(x) = \sqrt{x+3}$ represent?
   1. Shift right 3 units
   2. Shift left 3 units
   3. Shift up 3 units
   4. Shift down 3 units
2. What transformation does the function $f(x) = 2\sqrt{x}$ represent?
   1. Vertical compression by a factor of 2
   2. Vertical stretch by a factor of 2
   3. Horizontal compression by a factor of 2
   4. Horizontal stretch by a factor of 2
3. What transformation does the function $f(x) = \sqrt{x} - 1$ represent?
   1. Shift right 1 unit
   2. Shift left 1 unit
   3. Shift up 1 unit
   4. Shift down 1 unit
4. What transformation does the function $f(x) = -\sqrt{x}$ represent?
   1. Reflection over the y-axis
   2. Reflection over the x-axis
   3. Vertical stretch by a factor of -1
   4. Horizontal stretch by a factor of -1
5. What transformation does the function $f(x) = \sqrt{-x}$ represent?
   1. Reflection over the x-axis
   2. Reflection over the y-axis
   3. Vertical stretch by a factor of -1
   4. Horizontal stretch by a factor of -1
6. What transformations does the function $f(x) = 3\sqrt{x-2} + 1$ represent?
   1. Vertical stretch by 3, shift right 2, shift down 1
   2. Vertical stretch by 3, shift left 2, shift up 1
   3. Vertical stretch by 3, shift right 2, shift up 1
   4. Vertical compression by 3, shift right 2, shift up 1
7. What transformations does the function $f(x) = -\sqrt{x+4} - 2$ represent?
   1. Reflection over x-axis, shift left 4, shift down 2
   2. Reflection over y-axis, shift right 4, shift up 2
   3. Reflection over x-axis, shift right 4, shift up 2
   4. Reflection over y-axis, shift left 4, shift down 2