please help me determine
the equation of g(x) that results from translating the function f(x) = x^2 + 3 upward 7 units
To determine the equation of the function g(x) resulting from translating the function f(x) = x^2 + 3 upward by 7 units, you need to perform the translation on the function f(x) and express it mathematically.
First, let's understand what happens when we translate a function upward by a certain number of units. In this case, we are translating upward by 7 units. This means that for any point (x, y) on the graph of f(x), the corresponding point on the graph of g(x) will be (x, y + 7).
To find the equation for g(x), we need to substitute y + 7 for y in the equation of f(x).
Start with the equation of f(x) = x^2 + 3 and substitute y + 7 for y:
g(x) = x^2 + 3 + 7
Simplifying the equation:
g(x) = x^2 + 10
So, the equation for g(x) is g(x) = x^2 + 10. This equation represents the function resulting from translating f(x) = x^2 + 3 upward by 7 units.