1. The problem is to analyze and understand the given functions: 2. The functions are: 1. $y = x + 4$ 2. $y = |x|$ 3. $x = |y|^2$ 4. $y = -2(x+4)^2 - 1$ 3. Let's discuss each function: 4. For $y = x + 4$: - This is a linear function with slope 1 and y-intercept 4. - The graph is a straight line. 5. For $y = |x|$: - This is the absolute value function. - It outputs the non-negative value of $x$. - The graph is a V shape with vertex at the origin. 6. For $x = |y|^2$: - This can be rewritten as $x = (|y|)^2 = y^2$ since squaring removes the absolute value. - This is a parabola opening to the right. 7. For $y = -2(x+4)^2 - 1$: - This is a quadratic function with vertex at $(-4, -1)$. - The parabola opens downward because of the negative coefficient. 8. Summary: - 1st function: linear line. - 2nd function: V-shaped absolute value. - 3rd function: parabola opening right. - 4th function: downward parabola shifted left and down. Final answers are the descriptions and forms of these functions.