IDNLearn.com: Your trusted source for accurate and reliable answers. Our experts are available to provide in-depth and trustworthy answers to any questions you may have.
Sagot :
To solve the problem, we need to analyze the transformations applied to the function [tex]\( f(x) = x^2 \)[/tex] to transform it into a new function [tex]\( g \)[/tex].
1. Identify the Type of Transformation:
- The function [tex]\( f(x) = x^2 \)[/tex] has undergone a transformation resulting in a function [tex]\( g \)[/tex].
- The type of transformation applied is a "translation". This is the correct term for the movement of the entire graph horizontally or vertically without altering its shape or orientation.
2. Recognize the Expression of the Transformed Function:
- The general form for function transformation [tex]\( g \)[/tex] of [tex]\( f(x) \)[/tex] involving translation can be expressed as [tex]\( g(x) = f(x) ± k \)[/tex].
- For the function [tex]\( f(x) = x^2 \)[/tex], a vertical translation involves adding or subtracting a constant [tex]\( k \)[/tex].
3. Determine the Specific Translation Applied:
- According to the given anwer, the specific translation applied to [tex]\( x^2 \)[/tex] is a vertical translation by 3 units.
- The transformation [tex]\( g(x) \)[/tex] can be written as [tex]\( g(x) = f(x) ± 3 \)[/tex].
4. Construct the Final Form of the Transformed Function:
- Applying the translation to [tex]\( f(x) = x^2 \)[/tex]:
[tex]\[ g(x) = x^2 ± 3 \][/tex]
5. Fine-Tune the Equation Based on the Given Clues:
- The presence of [tex]\( ± \)[/tex] suggests that there might be flexibility in whether it is [tex]\( +3 \)[/tex] or [tex]\( -3 \)[/tex]. In our case, let's assume a positive translation:
[tex]\[ g(x) = x^2 + 3 \][/tex]
Therefore, the detailed selection is as follows:
Function [tex]\( g \)[/tex] is a "translation" of function [tex]\( f \)[/tex].
[tex]\[ g(x) = x^2 + 3 \][/tex]
1. Identify the Type of Transformation:
- The function [tex]\( f(x) = x^2 \)[/tex] has undergone a transformation resulting in a function [tex]\( g \)[/tex].
- The type of transformation applied is a "translation". This is the correct term for the movement of the entire graph horizontally or vertically without altering its shape or orientation.
2. Recognize the Expression of the Transformed Function:
- The general form for function transformation [tex]\( g \)[/tex] of [tex]\( f(x) \)[/tex] involving translation can be expressed as [tex]\( g(x) = f(x) ± k \)[/tex].
- For the function [tex]\( f(x) = x^2 \)[/tex], a vertical translation involves adding or subtracting a constant [tex]\( k \)[/tex].
3. Determine the Specific Translation Applied:
- According to the given anwer, the specific translation applied to [tex]\( x^2 \)[/tex] is a vertical translation by 3 units.
- The transformation [tex]\( g(x) \)[/tex] can be written as [tex]\( g(x) = f(x) ± 3 \)[/tex].
4. Construct the Final Form of the Transformed Function:
- Applying the translation to [tex]\( f(x) = x^2 \)[/tex]:
[tex]\[ g(x) = x^2 ± 3 \][/tex]
5. Fine-Tune the Equation Based on the Given Clues:
- The presence of [tex]\( ± \)[/tex] suggests that there might be flexibility in whether it is [tex]\( +3 \)[/tex] or [tex]\( -3 \)[/tex]. In our case, let's assume a positive translation:
[tex]\[ g(x) = x^2 + 3 \][/tex]
Therefore, the detailed selection is as follows:
Function [tex]\( g \)[/tex] is a "translation" of function [tex]\( f \)[/tex].
[tex]\[ g(x) = x^2 + 3 \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.