Suppose the graph of f is given describe how the graph of each function can be obtained from the graph of f?
F(x+9)
And F(x)+8
1. To obtain the graph of f(x+9) from the graph of f, you would shift the entire graph of f to the left by 9 units. This means that each point on the graph of f(x) would be moved 9 units to the left.
2. To obtain the graph of f(x)+8 from the graph of f, you would shift the entire graph of f vertically upwards by 8 units. This means that each point on the graph of f(x) would be moved 8 units upwards.
To obtain the graph of each function from the graph of f, we need to apply the given transformations.
1. For the function F(x+9):
- Shift the graph of f horizontally to the left by 9 units. This means that each point on the graph of f with coordinates (x, y) will be shifted to (x + 9, y).
2. For the function F(x)+8:
- Shift the graph of f vertically upwards by 8 units. This means that each point on the graph of f with coordinates (x, y) will be shifted to (x, y + 8).
Remember, in both cases, the shape and other attributes of the graph remain the same; only the position of the graph changes.
To obtain the graph of each function from the graph of f, we need to understand how the given operations affect the input variable or the output values.
1. F(x+9):
Adding 9 to the input variable (x) of the function f shifts the graph horizontally by 9 units to the left. This means that each point on the graph will be moved 9 units towards the left. For example, if a point on the graph of f was at (3, y), then on the graph of F(x+9), this point would be located at (3 - 9, y).
2. F(x) + 8:
Adding 8 to the output values of the function f shifts the graph vertically by 8 units upwards. This means that each point on the graph will be raised 8 units higher. For example, if a point on the graph of f was at (x, 5), then on the graph of F(x) + 8, this point would be located at (x, 5 + 8).
In summary, to obtain the graph of F(x+9) from the graph of f, shift the graph horizontally 9 units to the left. To obtain the graph of F(x) + 8 from the graph of f, shift the graph vertically 8 units upwards.