https://file.aiquickdraw.com/mathbot/file/1725779698641s3rnbu29.jpg

Let's analyze each function based on the table provided and determine if it is linear, quadratic, or exponential.

### **Función 1**
- \( x \) values: \( 0, 1, 2, 3, 4 \)
- \( y \) values: \( -5, 1, 7, 13, 19 \)

The difference between consecutive \( y \)-values:
- \( 1 - (-5) = 6 \)
- \( 7 - 1 = 6 \)
- \( 13 - 7 = 6 \)
- \( 19 - 13 = 6 \)

Since the difference is constant, **Función 1 is linear**.

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### **Función 2**
- \( x \) values: \( 1, 2, 3, 4, 5 \)
- \( y \) values: \( 8, 0, -8, -16, -24 \)

The difference between consecutive \( y \)-values:
- \( 0 - 8 = -8 \)
- \( -8 - 0 = -8 \)
- \( -16 - (-8) = -8 \)
- \( -24 - (-16) = -8 \)

Since the difference is constant, **Función 2 is linear**.

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### **Función 3**
- \( x \) values: \( 1, 2, 3, 4, 5 \)
- \( y \) values: \( -61, -34, -17, -8, -17 \)

Let's calculate the differences between consecutive \( y \)-values:
- \( -34 - (-61) = 27 \)
- \( -17 - (-34) = 17 \)
- \( -8 - (-17) = 9 \)
- \( -17 - (-8) = -9 \)

Since the differences between \( y \)-values are not constant, it is neither linear nor quadratic. It appears **Función 3 does not follow a recognizable pattern from the choices given**.

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### Summary of the functions:
1. **Función 1**: Linear
2. **Función 2**: Linear
3. **Función 3**: None of the given options

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Do you need more details or have any questions?

### 5 Related Questions:
1. What is the definition of a linear function?
2. How do quadratic functions differ from linear functions in terms of their rate of change?
3. What is the general form of an exponential function?
4. How can we identify a quadratic function from a table of values?
5. How does the second difference help in identifying quadratic functions?

### Tip:
When analyzing functions from a table, look for constant differences for linear functions, and constant second differences for quadratic functions. Exponential functions grow by a constant factor.

For each function, determine if it is linear, quadratic, or exponential.

Analyze tables to determine if the given functions are linear, quadratic, or exponential. Includes key concepts such as first differences for linear functions and second differences for quadratic functions. Ideal for students in Grades 8-10.

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