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.

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.

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.

Summary of the functions:

1. Función 1: Linear
2. Función 2: Linear
3. Función 3: None of the given options

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.