Determine the equation of g (x) that results from translating the function f(x)=x^2+5 upward 13 units.
To determine the equation of g(x), which is the result of translating the function f(x) = x^2 + 5 upward by 13 units, we need to understand how translation affects the function.
When translating a function upward (or downward), we only need to change the constant term (the y-intercept) of the function. Since we want to move f(x) upward by 13 units, we need to increase the value of the constant term by 13.
The original function, f(x) = x^2 + 5, has a constant term of 5. By increasing it by 13, we get the new constant term of g(x). Therefore, the equation of g(x) will be:
g(x) = x^2 + 5 + 13
Simplifying,
g(x) = x^2 + 18
So, the equation of g(x) is g(x) = x^2 + 18.
Note: The process of translating a function involves adjusting the entire graph, not just changing the equation. However, in this case, since the translation is purely vertical, we only need to modify the constant term.