Question

What is the correct description for the transformation from b(x)=3−12x−−−−−√
𝑏
(
𝑥
)
=
3
−
12
𝑥
to m(x)=34x−−√
𝑚
(
𝑥
)
=
3
4
𝑥
?(1 point)
Responses

horizontal compression by a factor of 13
1
3
and a reflection over the x-axis
horizontal compression by a factor of Start Fraction 1 over 3 End Fraction and a reflection over the x -axis

horizontal compression by a factor of 13
1
3
and a reflection over the y-axis
horizontal compression by a factor of Start Fraction 1 over 3 End Fraction and a reflection over the y -axis

horizontal stretch by a factor of 3 and a reflection over the x-axis
horizontal stretch by a factor of 3 and a reflection over the x -axis

horizontal stretch by a factor of 3 and a reflection over the y-axis

Answer 1

To analyze the transformation from \( b(x) = 3 - \sqrt{12x} \) to \( m(x) = \frac{3}{4} \sqrt{x} \), we need to break down the transformation step by step.

1. **Understand the original function:**
The function \( b(x) = 3 - \sqrt{12x} \) consists of a square root function multiplied by \( \sqrt{12} \), where \( 12 \) indicates a horizontal compression because the argument of the square root is multiplied by a factor of 12.

2. **Identify the basic transformation:**
The term \( \sqrt{12x} \) can be rewritten as \( \sqrt{12} \sqrt{x} \), which illustrates that \( \sqrt{x} \) is being compressed horizontally because multiplying \( x \) by 12 compresses the graph towards the y-axis.

3. **Transformation of the \( y \)-value:**
The transformation includes changing the vertical shift from 3 into a different function. The reflection over the x-axis occurs here because of the negative sign in front of \( \sqrt{12x} \) in the original function.

4. **Final steps towards the transformation:**
The transformation leads you to \( m(x) = \frac{3}{4} \sqrt{x} \). Upon comparing, you can observe that there is indeed a vertical compression too, as the output is multiplied by \( \frac{3}{4} \).

5. **Conclusion:**
The correct description for the transformation involves a horizontal compression by a factor of \( \frac{1}{3} \) and a reflection over the x-axis.

The correct response matches:
**Horizontal compression by a factor of \( \frac{1}{3} \) and a reflection over the x-axis.**