Explain how the graph of g is obtained from the graph of f
A.f(x)=(x),g(x)=(x+3)-3
B.f(x)=(x),g(x)=(x-3)+3
A. To obtain the graph of g from the graph of f, we can follow these steps:
1. Start with the graph of f(x) = x, which is a straight line passing through the origin with a slope of 1.
2. To obtain g(x), we need to add 3 to the input (x+3) and then subtract 3 from the result. So, g(x) = (x+3) - 3 = x.
3. Adding 3 to the input (x+3) shifts the graph of f three units to the left. This means that every point on the graph of f(x) is shifted three units to the left on the graph of g(x).
4. Then, subtracting 3 from the result (-3) brings the graph back to its original position. So, after this step, the graph of g(x) is back to its original position and is the same as the graph of f(x).
5. Therefore, the graph of g(x) = (x+3) - 3 is the same as the graph of f(x) = x.
B. To obtain the graph of g from the graph of f, we can follow these steps:
1. Start with the graph of f(x) = x, which is a straight line passing through the origin with a slope of 1.
2. To obtain g(x), we need to subtract 3 from the input (x-3) and then add 3 to the result. So, g(x) = (x-3) + 3 = x.
3. Subtracting 3 from the input (x-3) shifts the graph of f three units to the right. This means that every point on the graph of f(x) is shifted three units to the right on the graph of g(x).
4. Then, adding 3 to the result (+3) brings the graph back to its original position. So, after this step, the graph of g(x) is back to its original position and is the same as the graph of f(x).
5. Therefore, the graph of g(x) = (x-3) + 3 is the same as the graph of f(x) = x.
To obtain the graph of g from the graph of f, we need to apply the given transformation to each point on the graph of f.
In Case A, where f(x) = x and g(x) = (x + 3) - 3:
1. Starting with the graph of f, shift each point to the left by 3 units. This means that for every point (x, y) on the graph of f, we subtract 3 from the x-coordinate to get the corresponding point on the graph of g.
In Case B, where f(x) = x and g(x) = (x - 3) + 3:
1. Starting with the graph of f, shift each point to the right by 3 units. This means that for every point (x, y) on the graph of f, we add 3 to the x-coordinate to get the corresponding point on the graph of g.
Remember, shifting left means subtracting from the x-coordinate, while shifting right means adding to the x-coordinate.
To understand how the graph of g is obtained from the graph of f, we need to analyze the given equations:
A) f(x) = x, g(x) = (x + 3) - 3
B) f(x) = x, g(x) = (x - 3) + 3
In both cases, the equation f(x) = x represents a straight line with a slope of 1 passing through the origin (0,0) and extending indefinitely in both directions.
Let's analyze the two scenarios separately:
A) In equation A, g(x) = (x + 3) - 3, we can break it down into two parts: (x + 3) and (x + 3) - 3.
The term (x + 3) represents a horizontal shift of the graph of f to the left by 3 units. The entire graph of f will be shifted 3 units to the left.
Next, when we subtract 3 from (x + 3), we are decreasing the y-coordinate of each point on the graph by 3 units. This translates to a vertical shift of the graph downwards by 3 units.
Overall, the graph of g will be the same as the graph of f, but shifted 3 units to the left and 3 units downwards.
B) In equation B, g(x) = (x - 3) + 3, we can break it down into two parts: (x - 3) and (x - 3) + 3.
The term (x - 3) represents a horizontal shift of the graph of f to the right by 3 units. The entire graph of f will be shifted 3 units to the right.
Next, when we add 3 to (x - 3), we are increasing the y-coordinate of each point on the graph by 3 units. This translates to a vertical shift of the graph upwards by 3 units.
Overall, the graph of g will be the same as the graph of f, but shifted 3 units to the right and 3 units upwards.
In summary, the graph of g is obtained from the graph of f by applying horizontal and vertical shifts as indicated by the given equations.