Question

The function g(x) is more narrow than f(x) = (x + 2)^2 and is translated right 5 units and down 4 units from f(x). Which is a possible equation for g(x)?

a. g(x) = 1/2 (x + 3)^2 - 4

b. g(x) = 2(x + 3)^2 + 4

c. g(x) = 2(x - 3)^2 - 4

d. g(x) = 1/2 (x - 3)^2 + 4

Answer 1

The correct equation for g(x), which is more narrow than f(x)=(x+2)^2 and translated right by 5 units and down by 4 units, is g(x)=2(x-3)^2-4, which is option c.

Step-by-step explanation:

The function g(x) is a transformation of the function f(x) = (x + 2)^2, where g(x) is described as more narrow and is translated right 5 units and down 4 units from f(x).

A more narrow function means that the vertical stretch factor is greater than 1. Since f(x) is translated right by 5 units, we replace x with (x - 5) in the equation, and to translate down by 4 units, we subtract 4 from the entire function.

The correct transformation of f(x) to g(x) given these parameters would be g(x) = a(x - 3)^2 - 4, where 'a' is greater than 1 since the function is more narrow. Among the given options, the one that fulfills these conditions is option c: g(x) = 2(x - 3)^2 - 4.