The image contains four functions for which you are asked to draw the graphs. They are:

1. $f(x) = -x^2 + 2x - 1$
2. $y = |x| + x$
3. $|x| = |y|$
4. $y^2 = x$

Let’s briefly discuss each of these functions and how their graphs look:

1. $f(x) = -x^2 + 2x - 1$:
   This is a quadratic function in the form $ax^2 + bx + c$, with $a = -1$, $b = 2$, and $c = -1$. It represents a downward-opening parabola. We can find the vertex using the formula $x = -\frac{b}{2a}$ and then plot the points accordingly.

2. $y = |x| + x$:
   This function involves the absolute value of $x$, which behaves differently for positive and negative values of $x$. For $x \geq 0$, $y = 2x$, and for $x < 0$, $y = 0$.

3. $|x| = |y|$:
   This represents a symmetrical graph with respect to both the x-axis