Question

If the graph of the function h is defined by = h(x)+x^2+9 is translated vertically downward by 9 units, it becomes the graph of a function g. Find the expression for
gx

Answer 1

The answer is g(x) = x².
Solution:
The graph of h(x) = x²+9 translated vertically downward by 9 units means that each point (x, h(x)) is shifted onto the point (x, h(x) - 9), that is, 
     (x, h(x)) → (x, h(x) - 9)
The translated graph that represents the function is defined by the expression for g(x):
     g(x) = h(x) - 9 = x² + 9 - 9 = x²

h(x) = x²+9 → g(x) = x² shows that the graph of the equation g(x) = x² moves the graph of h(x) = x²+9 down nine units.