Question

Which could be the function graphed below

Answer 1

y= sqrt(x+4)

Explanation:

The reason is because the function is translated horizontally to the left.

The base function is y=sqrt(x)

The option A. f(x) sqrt (x-5) + 1, the graph should be translated horizontally 5 units to the right. It's not the case. And translated 1 unit vertically.

Option B. f(x) = sqrt (x-2) the graph should be translated horizontally 2 units to the right. It's not the case.

Option C. f(x) = sqrt(x), the graph should start at x=0. It's not the case.

The option D. f(x) = sqrt(x+4), the function is translated 4 times horizontally to the left. So this is the case.

Answer 2

`f(x) = √(x + 4)`

EXPLANATION

The parent function is

`f(x) = √(x)`

This parent function has been shifted to the left, hence its transformation is of the form,

`f(x + k)`

The only option in this form is the last option,

`f(x) = √(x + 4)`