Answered

Get the most out of your questions with IDNLearn.com's extensive resources. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

Which of the following describes the graph of [tex]\( y = \sqrt{-4x - 36} \)[/tex] compared to the parent square root function?

A. Stretched by a factor of 2, reflected over the x-axis, and translated 9 units right.
B. Stretched by a factor of 2, reflected over the x-axis, and translated 9 units left.
C. Stretched by a factor of 2, reflected over the y-axis, and translated 9 units right.
D. Stretched by a factor of 2, reflected over the y-axis, and translated 9 units left.

Sagot :

GinnyAnsweridn
To understand how the graph of the function [tex]\( y = \sqrt{-4x - 36} \)[/tex] is transformed compared to the parent function [tex]\( y = \sqrt{x} \)[/tex], we need to examine each component of the function in detail.

First, let's rewrite the function in a more recognizable form:
[tex]\[ y = \sqrt{-4(x + 9)} \][/tex]

Now, we can break this down:

1. Inside the square root function:
- The term [tex]\(-4\)[/tex] inside the square root can be analyzed in pieces. The term [tex]\( -4x \)[/tex] indicates two transformations:
- The negative sign reflects the graph over the [tex]\( y \)[/tex]-axis.
- The coefficient [tex]\(-4\)[/tex] can be interpreted as affecting the horizontal scaling. Since the [tex]\( x \)[/tex] axis is scaled by a factor of 4 inside the square root, it results in horizontal compression by a factor of [tex]\( \frac{1}{2} \)[/tex].

2. Horizontal compression by a factor of [tex]\( \frac{1}{2} \)[/tex]:
- The function [tex]\( y = \sqrt{-4x} \)[/tex] compresses horizontally, but this appears as if the graph is stretched in the opposite direction compared to the parent function.

3. Reflection over the [tex]\( y \)[/tex]-axis:
- The negative sign in front of the [tex]\( 4x \)[/tex] means that instead of opening to the right, the graph opens to the left, reflecting over the [tex]\( y \)[/tex]-axis.

4. Horizontal translation:
- The [tex]\( (x + 9) \)[/tex] inside the function translates the graph horizontally by [tex]\( -9 \)[/tex] units. This means the graph is shifted 9 units to the left.

Putting these transformations together, we determine that the transformations are as follows:
- The graph is stretched horizontally by a factor of 2 (compression in the [tex]\( x \)[/tex]-direction).
- The graph is reflected over the [tex]\( y \)[/tex]-axis.
- The graph is translated 9 units to the left.

Thus, the correct option that describes the transformation is:
- stretched by a factor of 2, reflected over the [tex]\( y \)[/tex]-axis, and translated 9 units left

So, the answer is:
4. stretched by a factor of 2 , reflected over the [tex]\( y \)[/tex]-axis, and translated 9 units left
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.