# Curves, relationships, functions and symmetry

1. Sep 3, 2010

### mariechap89

For the following curves i) y=x^2+4x-1 ii) y=-2+or-Square root(x+5)
a) Sketch both the curves on the same sheet of graph paper- against the same axis
I have done this, although I have not shown it here

b) Determine with proof, whether the above curves are related.
Not sure how to do this.

c)Determine with proof, if either of the above curves are a function
Not sure how to do this either.

d)Determine, with proof, whether either of the curves displays odd or even symmetry
y=f(x)=x^2+4x-1
f(-x)=-x^2+4x-1
Even function
Is this correct

Any help would be great thanks

2. Sep 3, 2010

### Staff: Mentor

What did you notice about the two graphs in part a?
Surely you have learned how to tell whether a graph represents a function. Does the phrase "vertical line test" ring a bell?
A function is even if f(-x) = f(x) for all x in the domain of the function. A function is odd if -f(-x) = f(x) for all x in the domain of the function. You have not calculated f(-x) correctly. Please try again.

3. Sep 3, 2010

### HallsofIvy

Staff Emeritus
If $y= 2\pm\sqrt{x+ 5}$ then $y- 2= \pm\sqrt{x+ 5}$ and, squaring both sides, $(y- 2)^2= y^2- 4y+ 4= x+ 5$ which is exactly the same as $y^2- 4y- 1= x$. How is that formula connected to $y= x^2- 4y+ 1$?