From personal advice to professional guidance, IDNLearn.com has the answers you seek. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
Sagot :
To determine which transformation was not done to convert the linear parent function \( f(x) = x \) to the function \( g(x) = -5(x + 3) - 8 \), let's analyze each component of the transformation step-by-step.
1. Inside the Parentheses \((x+3)\):
- The expression \( (x+3) \) indicates a horizontal shift. When we add 3 to \( x \), it translates the graph to the left by 3 units.
- Shift to the left by 3 units.
2. Multiplication by a Negative Coefficient and a Factor \(-5\):
- The multiplication by -5 outside the parentheses performs two operations on the graph:
- The negative sign indicates a reflection over the \( x \)-axis.
- The factor 5 represent a vertical stretch by a factor of 5.
- Reflection over the \( x \)-axis.
- Vertical stretch by a factor of 5.
3. Subtraction Outside the Parentheses (−8):
- Subtraction of 8 outside the parentheses indicates a vertical shift downward by 8 units.
- Shift down by 8 units.
Given the transformations, let's match them with the provided options:
A. Shift right 3 units:
- From our analysis, the function \( (x + 3) \) shifts the graph left by 3 units, not right. So, shift right by 3 units is not performed.
B. Vertical stretch by a factor of 5:
- This transformation is indeed done, as indicated by the coefficient 5. So, vertical stretch by a factor of 5 is performed.
C. Reflection over the \( x \)-axis:
- This transformation is also performed, as indicated by the negative sign. So, reflection over the \( x \)-axis is performed.
D. Shift down 8 units:
- The subtraction of 8 indicates that this transformation is done. So, shift down by 8 units is performed.
Based on the analysis, the transformation that was not done is:
A. Shift right 3 units.
1. Inside the Parentheses \((x+3)\):
- The expression \( (x+3) \) indicates a horizontal shift. When we add 3 to \( x \), it translates the graph to the left by 3 units.
- Shift to the left by 3 units.
2. Multiplication by a Negative Coefficient and a Factor \(-5\):
- The multiplication by -5 outside the parentheses performs two operations on the graph:
- The negative sign indicates a reflection over the \( x \)-axis.
- The factor 5 represent a vertical stretch by a factor of 5.
- Reflection over the \( x \)-axis.
- Vertical stretch by a factor of 5.
3. Subtraction Outside the Parentheses (−8):
- Subtraction of 8 outside the parentheses indicates a vertical shift downward by 8 units.
- Shift down by 8 units.
Given the transformations, let's match them with the provided options:
A. Shift right 3 units:
- From our analysis, the function \( (x + 3) \) shifts the graph left by 3 units, not right. So, shift right by 3 units is not performed.
B. Vertical stretch by a factor of 5:
- This transformation is indeed done, as indicated by the coefficient 5. So, vertical stretch by a factor of 5 is performed.
C. Reflection over the \( x \)-axis:
- This transformation is also performed, as indicated by the negative sign. So, reflection over the \( x \)-axis is performed.
D. Shift down 8 units:
- The subtraction of 8 indicates that this transformation is done. So, shift down by 8 units is performed.
Based on the analysis, the transformation that was not done is:
A. Shift right 3 units.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.