The graph of g(x) is f(x) translated to the right 7 units and up 2 units. What is the function rule for g(x)given f(x)=x2
The function rule for g(x) given f(x) = x^2 and translated to the right 7 units and up 2 units can be written as:
g(x) = (x - 7)^2 + 2
To translate the graph of f(x) to the right by 7 units, we substitute x with (x - 7) in the function rule.
Therefore, the function rule for g(x) is g(x) = (x - 7)^2, since f(x) = x^2.
To further translate the graph of f(x) upwards by 2 units, we add 2 to the entire function rule.
Hence, the final function rule for g(x) is g(x) = (x - 7)^2 + 2.
To find the function rule for g(x), which is a translation of f(x) to the right 7 units and up 2 units, you need to apply the translation to the original function f(x).
First, let's consider the translation to the right 7 units. To achieve this, you need to subtract 7 from the input variable x. So the new input variable becomes (x - 7).
Next, let's consider the translation up 2 units. To achieve this, you need to add 2 to the output variable f(x). So the new output variable becomes (f(x) + 2).
Combining these translations, the function rule for g(x) can be written as:
g(x) = f(x - 7) + 2
Since the original function is f(x) = x^2, we substitute it into the function rule for g(x):
g(x) = (x - 7)^2 + 2
Therefore, the function rule for g(x) is g(x) = (x - 7)^2 + 2.