Question

Given the function f(x) = x² + 5 , if the graph g(x) undergoes a right shift of 2 and a downward shift of 3, the equation modeling g(x) is:

a) g(x) = (x - 2)² + 2
b) g(x) = x² + 3
c) g(x) = (x + 2)² - 3
d) g(x) = (x + 2)² - 8

Answer 1

The equation modeling g(x) after undergoing a right shift of 2 and a downward shift of 3 is g(x) = (x - 2)² + 2. Hence the correct answer is option A

Step-by-step explanation:

To find the equation modeling g(x), which is the graph of f(x) that undergoes a right shift of 2 and a downward shift of 3, we need to apply the corresponding transformations to the original function f(x) = x² + 5. A right shift of 2 means replacing x with (x - 2) and a downward shift of 3 means subtracting 3 from the function. Thus, the equation modeling g(x) is g(x) = (x - 2)² + 2, option a.