Answer :
To solve the question about the transformation of the graph of the function [tex]\( y = f(x+62) \)[/tex], we need to understand how changes inside the function's argument affect the graph.
1. Identify the Transformation Type:
- The function [tex]\( y = f(x+c) \)[/tex] involves a horizontal shift.
- If [tex]\( c \)[/tex] is positive, the graph shifts to the left by [tex]\( c \)[/tex] units.
- If [tex]\( c \)[/tex] is negative, the graph shifts to the right by the magnitude of [tex]\( c \)[/tex] units.
2. Apply this Understanding:
- In the given function [tex]\( y = f(x+62) \)[/tex], the argument [tex]\( x \)[/tex] has been replaced by [tex]\( x+62 \)[/tex].
- Here, [tex]\( c = 62 \)[/tex], which is a positive number.
3. Determine the Direction of the Shift:
- According to our transformation rule: If [tex]\( c \)[/tex] is positive, shift the graph to the left.
- Therefore, the transformation [tex]\( y = f(x+62) \)[/tex] results in the graph of [tex]\( y = f(x) \)[/tex] shifting to the left by 62 units.
By following these steps, we conclude that the action required to obtain the graph of [tex]\( y = f(x+62) \)[/tex] from [tex]\( y = f(x) \)[/tex] is shifting the graph of [tex]\( f(x) \)[/tex] to the left 62 units.
1. Identify the Transformation Type:
- The function [tex]\( y = f(x+c) \)[/tex] involves a horizontal shift.
- If [tex]\( c \)[/tex] is positive, the graph shifts to the left by [tex]\( c \)[/tex] units.
- If [tex]\( c \)[/tex] is negative, the graph shifts to the right by the magnitude of [tex]\( c \)[/tex] units.
2. Apply this Understanding:
- In the given function [tex]\( y = f(x+62) \)[/tex], the argument [tex]\( x \)[/tex] has been replaced by [tex]\( x+62 \)[/tex].
- Here, [tex]\( c = 62 \)[/tex], which is a positive number.
3. Determine the Direction of the Shift:
- According to our transformation rule: If [tex]\( c \)[/tex] is positive, shift the graph to the left.
- Therefore, the transformation [tex]\( y = f(x+62) \)[/tex] results in the graph of [tex]\( y = f(x) \)[/tex] shifting to the left by 62 units.
By following these steps, we conclude that the action required to obtain the graph of [tex]\( y = f(x+62) \)[/tex] from [tex]\( y = f(x) \)[/tex] is shifting the graph of [tex]\( f(x) \)[/tex] to the left 62 units.
