Asked by Jaz
What transformations produce the graph of g left parenthesis x right parenthesis equals negative start absolute value 3x right absolute value from the graph of the parent function f left parenthesis x right parenthesis equals start absolute value x right absolute value? Select all that apply.
(1 point)
Responses
reflection over the x-axis
reflection over the x -axis
reflection over the y-axis
reflection over the y -axis
horizontal stretch by a factor of 3
horizontal stretch by a factor of 3
horizontal compression by a factor of 3
horizontal compression by a factor of 3
vertical stretch by a factor of 3
vertical stretch by a factor of 3
vertical compression by a factor of 3
(1 point)
Responses
reflection over the x-axis
reflection over the x -axis
reflection over the y-axis
reflection over the y -axis
horizontal stretch by a factor of 3
horizontal stretch by a factor of 3
horizontal compression by a factor of 3
horizontal compression by a factor of 3
vertical stretch by a factor of 3
vertical stretch by a factor of 3
vertical compression by a factor of 3
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the transformations that produce the graph of \( g(x) = -|3x| \) from the parent function \( f(x) = |x| \), we can consider the following pieces:
1. **Horizontal Stretch by a Factor of 3**: The function \( |3x| \) can be seen as a horizontal compression of \( |x| \) by a factor of \( \frac{1}{3} \) (since it "compresses" the x-values by multiplying them by 3). Therefore, this transformation does not apply.
2. **Horizontal Compression by a Factor of 3**: This is correct. The term \( 3x \) means that every x-value in the original function is compressed toward the y-axis by a factor of 3.
3. **Reflection over the x-axis**: The negative sign in front of the absolute value function indicates a reflection over the x-axis. So this transformation does apply.
4. **Reflection over the y-axis**: There is no negative sign in front of \( x \) itself, so there is no reflection over the y-axis. This transformation does not apply.
5. **Vertical Stretch by a Factor of 3**: The term \( |3x| \) does not produce a vertical stretch by a factor of 3; instead, it affects the horizontal scaling. So this transformation does not apply.
6. **Vertical Compression by a Factor of 3**: Similarly, there is no vertical compression happening; the negative sign only reflects it over the x-axis. So this transformation does not apply.
Based on the information above, the transformations that apply are:
- **Reflection over the x-axis**
- **Horizontal compression by a factor of 3**
1. **Horizontal Stretch by a Factor of 3**: The function \( |3x| \) can be seen as a horizontal compression of \( |x| \) by a factor of \( \frac{1}{3} \) (since it "compresses" the x-values by multiplying them by 3). Therefore, this transformation does not apply.
2. **Horizontal Compression by a Factor of 3**: This is correct. The term \( 3x \) means that every x-value in the original function is compressed toward the y-axis by a factor of 3.
3. **Reflection over the x-axis**: The negative sign in front of the absolute value function indicates a reflection over the x-axis. So this transformation does apply.
4. **Reflection over the y-axis**: There is no negative sign in front of \( x \) itself, so there is no reflection over the y-axis. This transformation does not apply.
5. **Vertical Stretch by a Factor of 3**: The term \( |3x| \) does not produce a vertical stretch by a factor of 3; instead, it affects the horizontal scaling. So this transformation does not apply.
6. **Vertical Compression by a Factor of 3**: Similarly, there is no vertical compression happening; the negative sign only reflects it over the x-axis. So this transformation does not apply.
Based on the information above, the transformations that apply are:
- **Reflection over the x-axis**
- **Horizontal compression by a factor of 3**
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