Answer :
To solve the problem, we need to understand how transformations affect the graph of a function. Specifically, we're looking at what happens to the graph of [tex]\( y = f(x) \)[/tex] when it changes to [tex]\( y = f(x) - 84 \)[/tex].
1. Understand the transformation:
- The expression [tex]\( y = f(x) - 84 \)[/tex] indicates a vertical transformation. Subtracting a number from a function, [tex]\( y = f(x) - 84 \)[/tex], means we are moving every point on the graph of [tex]\( y = f(x) \)[/tex] downward.
2. Determine the direction:
- Instead of going horizontally (right or left), changes that involve a subtraction of a constant outside the function itself, like [tex]\( f(x) - 84 \)[/tex], affect the graph vertically.
- In this case, since we are subtracting 84, each point on the graph of [tex]\( y = f(x) \)[/tex] moves 84 units _downwards_.
3. Choose the correct action:
- Among the given options:
- Shifting to the right or to the left affects the x-coordinate and involves changes inside the function argument like [tex]\( f(x - c) \)[/tex] or [tex]\( f(x + c) \)[/tex].
- Shifting upwards 84 units would be represented by an addition, [tex]\( y = f(x) + 84 \)[/tex].
- Thus, shifting the graph of [tex]\( f(x) \)[/tex] downwards by 84 units is the correct transformation to obtain [tex]\( y = f(x) - 84 \)[/tex].
Therefore, the correct action to obtain the graph of [tex]\( y = f(x) - 84 \)[/tex] from [tex]\( y = f(x) \)[/tex] is to shift the graph of [tex]\( f(x) \)[/tex] downwards 84 units.
1. Understand the transformation:
- The expression [tex]\( y = f(x) - 84 \)[/tex] indicates a vertical transformation. Subtracting a number from a function, [tex]\( y = f(x) - 84 \)[/tex], means we are moving every point on the graph of [tex]\( y = f(x) \)[/tex] downward.
2. Determine the direction:
- Instead of going horizontally (right or left), changes that involve a subtraction of a constant outside the function itself, like [tex]\( f(x) - 84 \)[/tex], affect the graph vertically.
- In this case, since we are subtracting 84, each point on the graph of [tex]\( y = f(x) \)[/tex] moves 84 units _downwards_.
3. Choose the correct action:
- Among the given options:
- Shifting to the right or to the left affects the x-coordinate and involves changes inside the function argument like [tex]\( f(x - c) \)[/tex] or [tex]\( f(x + c) \)[/tex].
- Shifting upwards 84 units would be represented by an addition, [tex]\( y = f(x) + 84 \)[/tex].
- Thus, shifting the graph of [tex]\( f(x) \)[/tex] downwards by 84 units is the correct transformation to obtain [tex]\( y = f(x) - 84 \)[/tex].
Therefore, the correct action to obtain the graph of [tex]\( y = f(x) - 84 \)[/tex] from [tex]\( y = f(x) \)[/tex] is to shift the graph of [tex]\( f(x) \)[/tex] downwards 84 units.
