Question
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.f(x)=(x),g(x)=(x+3)-3
B.f(x)=(x),g(x)=(x-3)+3
Answers
GPT 3.5
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.
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.