To create a function \( g(x) \) that is 5 units up from another function \( f(x) \), you can simply add 5 to the original function.
For example, if you have a function \( f(x) \), the function \( g(x) \) would be defined as:
\[ g(x) = f(x) + 5 \]
This means that for each value of \( x \), the value of \( g(x) \) is 5 units greater than the value of \( f(x) \).
Here's how you might express this in code, such as in Python:
def f(x):
# Example of an original function, let's say f(x) = x^2
return x ** 2
def g(x):
return f(x) + 5
# Example usage
x_value = 3
print("g({}) = {}".format(x_value, g(x_value)))
In this example, if \( f(x) = x^2 \), then \( g(x) = x^2 + 5 \). You can replace \( f(x) \) with any other function to adjust accordingly.