The image contains four mathematical functions for which you are being asked to draw graphs. Here's a breakdown of each:

1. Function 1: $f(x) = -x^2 + 2x - 1 \quad \forall x \in \mathbb{R}$ This is a quadratic function, which represents a parabola opening downwards since the coefficient of $x^2$ is negative.

2. Function 2: $y = |x| + x$ This function is piecewise since the absolute value will behave differently for positive and negative $x$:

   • When $x \geq 0$, $y = 2x$.
   • When $x < 0$, $y = 0$.

3. Function 3: $|x| = |y|$ This represents a pair of linear functions:

   • $y = x$
   • $y = -x$ It forms an X-shape on the graph.

4. Function 4: $y^2 = x$ This is a sideways parabola, where the square of $y$ is equal to $x$, meaning the graph opens to the right.

I will now prepare graphs for these functions.