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The image contains a list of equations involving different types of functions. I'll go through each one and classify them based on their structure:

1. **Linear function**:  
   \[ y = -3x + 5 \]
   This is a linear equation, where the slope is -3, and the y-intercept is 5.

2. **Quadratic function**:  
   \[ y = x^2 + 4x + 4 \]
   This is a quadratic equation, a parabola opening upwards since the coefficient of \(x^2\) is positive.

3. **Square root function**:  
   \[ y = \sqrt{9 - x} \]
   This is a square root function, defined for values of \(x\) where \(9 - x \geq 0\), i.e., \(x \leq 9\).

4. **Quadratic function (downward-opening)**:  
   \[ y = -4x^2 \]
   This is another quadratic function, but it opens downwards because the coefficient of \(x^2\) is negative.

5. **Rational function**:  
   \[ y = \frac{2}{x + 3} \]
   This is a rational function, with a vertical asymptote at \(x = -3\).

6. **Rational function with square root**:  
   \[ y = \frac{1}{\sqrt{x - 2}} \]
   This function is defined for \(x > 2\), as the square root must be positive.

7. **Rational function**:  
   \[ y = \frac{4x - 3}{2x + 6} \]
   This is another rational function, with a vertical asymptote where the denominator \(2x + 6 = 0\), i.e., \(x = -3\).

8. **Square root function**:  
   \[ y = \sqrt{x - 9} \]
   This square root function is defined for \(x \geq 9\).

Let me know if you'd like further details on any specific function or a graphical interpretation. Here are some follow-up questions:

1. How do you find the domain and range for the square root functions?
2. Can you identify any asymptotes in the rational functions?
3. What is the vertex form of the quadratic equation in problem 2?
4. How do the coefficients of the quadratic functions affect the direction of the parabola?
5. What is the solution to the rational equation in problem 7 when \(y = 0\)?

**Tip**: To analyze the behavior of functions, look for key features like intercepts, asymptotes, and domain restrictions based on the function type.

The image contains a list of equations involving different types of functions. The user wants to classify and analyze these functions.

This page analyzes a set of equations, including linear, quadratic, square root, and rational functions. Detailed explanations on their properties, such as slope, asymptotes, and domains, are provided. Suitable for Grades 9-12 math students.

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