Parent functions and their graphs with domain, range, and end behavior.

It looks like you've uploaded a reference chart of parent functions, which includes their equations, graphs, domains, ranges, and end behaviors. However, there is no specific problem or question included in your message.

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1. What task or problem you want me to solve using this chart?
2. Are you asking for:
- Identification of a function based on its graph?
- Analysis of transformations (e.g., shifts, stretches)?
- Determining domain/range/end behavior of a given function?
- Matching a function to its graph?
- Or something else?

Please provide the specific question or task related to this chart, and I’ll solve it step-by-step with clear explanations.

For now, here’s a summary of what this chart shows:

Key Parent Functions Included:

| Function Type | Equation | Key Features |
|---------------|---------|-------------|
| Linear | $ y = x $ | Odd, straight line through origin |
| Quadratic | $ y = x^2 $ | Even, parabola opening up |
| Cubic | $ y = x^3 $ | Odd, S-shaped curve |
| Absolute Value | $ y = |x| $ | V-shaped, even |
| Square Root | $ y = \sqrt{x} $ | Domain: $ [0, \infty) $, increasing |
| Cube Root | $ y = \sqrt[3]{x} $ | Defined for all real numbers, odd |
| Exponential | $ y = b^x, b > 1 $ | Always positive, increases rapidly |
| Logarithmic | $ y = \log_b(x), b > 1 $ | Only defined for $ x > 0 $, increases slowly |
| Rational (Inverse) | $ y = \frac{1}{x} $ | Hyperbola, asymptotes at axes |
| Rational (Inverse Squared) | $ y = \frac{1}{x^2} $ | U-shaped near origin, always positive |
| Greatest Integer (Floor) | $ y = \lfloor x \rfloor $ | Step function |
| Constant | $ y = C $ | Horizontal line |

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Once you tell me the actual problem (e.g., "Identify the parent function from this graph", or "Describe the transformation from $ y = x^2 $ to $ y = -(x-2)^2 + 3 $"), I can give a detailed solution.

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