# Reflections of Functions

1. Nov 3, 2007

### HelloMotto

1. The problem statement, all variables and given/known data
Given f(x)= square root of x - 4, write the equation for -f(x) and f(-x).
Sketch the three graphs on the same set of axes
Determine any points that are invariant for each reflection

3. The attempt at a solution
well basically I did the first part of the question and the result i got was
-f(x) = -square root of X + 4
f(-x) = square root of -x -4

the second part where it asks to graph these 3 equations, I've graphed the f(x) equation and the -f(x) equation but I can't graph the f(-x) equation. Simply because i get an error when i try to square root a negative number. So how would i graph this kind of eqation?

2. Nov 3, 2007

### rock.freak667

...-f(x) is a reflection in the x-axis
and f(-x) is a reflection in the y-axis

3. Nov 3, 2007

### HallsofIvy

Staff Emeritus
Do mean f(x)= sqrt(x+ 4) or f(x)= sqrt(x)+ 4?
If the first, the domain of f is $x+4\ge 0$ or $x \ge -4$ and f(-x) = sqrt(-x+ 4) has domain $-x+4\ge 0$ or $x\le 4$

If the second, the domain of f is $x\ge 0$ and f(-x)= sqrt(-x)+ 4 has domain $x\le 0$.

You have to take values of x in the correct domain in order to graph f(-x). In any case, rock.freak667 is correct: the graph of f(-x) is the refection of the graph of f(x) in the y-axis.