Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To describe the transformation from the parent cubic function [tex]\( y = x^3 \)[/tex] to the function [tex]\( y = -x + 3 \)[/tex], we need to analyze the changes applied to the graph of the original function.
1. Reflection over the y-axis: In the original cubic function [tex]\( y = x^3 \)[/tex], we get a reflection over the y-axis when we negate the variable [tex]\( x \)[/tex]. Thus, if we consider [tex]\( y = (-x)^3 \)[/tex], it would still be [tex]\( y = -x^3 \)[/tex]. In the given function [tex]\( y = -x + 3 \)[/tex], the presence of [tex]\( -x \)[/tex] indicates a reflection over the y-axis.
2. Vertical Shift: Next, let's look at the constant term in the transformed function [tex]\( y = -x + 3 \)[/tex]. This [tex]\( +3 \)[/tex] indicates that the entire graph of the function has been shifted vertically. A positive constant added to the function implies an upward shift. Therefore, the graph is shifted up by 3 units.
Based on this analysis, we can select the correct transformations as follows:
- Reflection over the y-axis
- Shift up 3 units
Thus, the correct options are:
1. Reflection over the y-axis
2. Shift up 3 units
1. Reflection over the y-axis: In the original cubic function [tex]\( y = x^3 \)[/tex], we get a reflection over the y-axis when we negate the variable [tex]\( x \)[/tex]. Thus, if we consider [tex]\( y = (-x)^3 \)[/tex], it would still be [tex]\( y = -x^3 \)[/tex]. In the given function [tex]\( y = -x + 3 \)[/tex], the presence of [tex]\( -x \)[/tex] indicates a reflection over the y-axis.
2. Vertical Shift: Next, let's look at the constant term in the transformed function [tex]\( y = -x + 3 \)[/tex]. This [tex]\( +3 \)[/tex] indicates that the entire graph of the function has been shifted vertically. A positive constant added to the function implies an upward shift. Therefore, the graph is shifted up by 3 units.
Based on this analysis, we can select the correct transformations as follows:
- Reflection over the y-axis
- Shift up 3 units
Thus, the correct options are:
1. Reflection over the y-axis
2. Shift up 3 units
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.