Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To transform the graph of [tex]\( f(x) = x^2 \)[/tex] to the graph of [tex]\( g(x) = (x-3)^2 + 2 \)[/tex], we need to apply the following transformations:
1. Horizontal Translation:
- The term [tex]\((x-3)\)[/tex] inside the square function indicates a horizontal translation.
- Since the expression inside the parenthesis is [tex]\( x - 3 \)[/tex], it implies that every point on the graph of [tex]\( f(x) \)[/tex] is shifted to the right by 3 units.
Therefore, the horizontal translation is 3 units to the right.
2. Vertical Translation:
- The constant [tex]\( +2 \)[/tex] outside the square function indicates a vertical translation.
- This means that every point on the graph of [tex]\( f(x) \)[/tex] is shifted upwards by 2 units.
Therefore, the vertical translation is 2 units upwards.
In conclusion:
- Horizontal translation of 3 units to the right.
- Vertical translation of 2 units upwards.
1. Horizontal Translation:
- The term [tex]\((x-3)\)[/tex] inside the square function indicates a horizontal translation.
- Since the expression inside the parenthesis is [tex]\( x - 3 \)[/tex], it implies that every point on the graph of [tex]\( f(x) \)[/tex] is shifted to the right by 3 units.
Therefore, the horizontal translation is 3 units to the right.
2. Vertical Translation:
- The constant [tex]\( +2 \)[/tex] outside the square function indicates a vertical translation.
- This means that every point on the graph of [tex]\( f(x) \)[/tex] is shifted upwards by 2 units.
Therefore, the vertical translation is 2 units upwards.
In conclusion:
- Horizontal translation of 3 units to the right.
- Vertical translation of 2 units upwards.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.