Worksheet for identifying parent functions by matching graphs to their equations.

Okay, I can see the issue clearly now. The graph in the third row, fourth column, shows a "V" shape, which is characteristic of an absolute value function. However, the equation provided below it is y = -(3x+1)² - 5, which is a quadratic function (because of the squared term). This is a mismatch between the graph and the equation.

This appears to be an error in the worksheet. The graph should either be a parabola (for the given quadratic equation) or the equation should be an absolute value function (like y = -|3x+1| - 5) to match the "V" shaped graph.

For the purpose of completing this task, I will categorize each graph based on its visual appearance rather than the potentially incorrect equation.

Let me now summarize all 16 graphs by their parent function type based on visual analysis:

Linear Functions:
- Row 1, Graph 3: Straight line
- Row 2, Graph 1: Straight line (y = x)
- Row 4, Graph 2: Straight line with negative slope (y = 2x - 9)
- Row 4, Graph 3: Horizontal line (y = √7, constant function)

Quadratic Functions:
- Row 1, Graph 2: Parabola opening up (y = x²)
- Row 2, Graph 3: Parabola opening down (y = -2x² + 4)
- Row 3, Graph 1: Parabola opening down (y = -x²)
- Row 3, Graph 3: Parabola opening up (y = x²)
- Row 4, Graph 4: Parabola opening down (y = -x² + 6)

Absolute Value Functions:
- Row 1, Graph 1: "V" shape (y = |x|)
- Row 2, Graph 2: "V" shape (y = |-2x| + 6)
- Row 3, Graph 2: "V" shape (y = |√(3x-4) + 2|)
- Row 3, Graph 4: "V" shape (mismatched equation, but graph is absolute value)
- Row 4, Graph 1: "V" shape (y = -|x+1| + 1)

Square Root Functions:
- Row 1, Graph 4: Curve starting at origin (y = √x)
- Row 2, Graph 4: Curve starting at a point on x-axis (y = (1/2)√x - 7)

I have now identified all 16 functions. To complete the task, I need to assign a different color to each type. Since there are four types, I'll assign one color to each:
- Linear: Blue
- Quadratic: Red
- Absolute Value: Green
- Square Root: Yellow

The solution is to color each graph according to its parent function type as identified above.