Question

The function g(x) is more narrow than f(x) = (x + 5)^2 and is translated right 6 units and down 2 units from f(x). Which is a possible equation for g(x)?

a) g(x) = (x + 5)^2 - 6
b) g(x) = (x - 5)^2 - 2
c) g(x) = (x + 11)^2 - 8
d) g(x) = (x - 11)^2 - 6

Answer 1

The equation for the function g(x) that is more narrow than f(x) = (x + 5)^2 and translated right 6 units and down 2 units from f(x) is g(x) = a(x - 6)^2 - 2, where 'a' is a fraction less than 1.

Step-by-step explanation:

To find the equation for the function g(x) which is more narrow than f(x) = (x + 5)^2 and translated right 6 units and down 2 units from f(x), we need to apply the transformations to the equation of f(x).

To make the function more narrow, we can multiply the x-term by a fraction less than 1, which will compress the graph horizontally. To translate the graph right 6 units, we subtract 6 from x in the equation. And to translate the graph down 2 units, we subtract 2 from the y-term of the equation.

Using these transformations, the equation for g(x) would be g(x) = a(x - 6)^2 - 2, where 'a' is a fraction less than 1 to make the graph narrower.