**Unlocking the Secrets of Functions: Unveiling the Mystery of f(5)**

Have you ever stumbled upon a table of values that left you scratching your head, wondering what function they represented? Fear not, dear reader, for we shall embark on a journey to decipher the enigmas of functions and unravel the secrets hidden within those mysterious tables. Join us as we delve into the world of functions and discover the answer to the perplexing question: “What is f(5)?”

The table of values, with its neatly arranged rows and columns, serves as a cryptic message, a puzzle waiting to be solved. The function, like a skilled magician, conceals its true nature, leaving us with tantalizing clues. But fear not, for with a keen eye and a touch of mathematical finesse, we shall unveil the hidden patterns and reveal the underlying function.

Our quest begins with understanding the concept of a function. A function is a mathematical entity that assigns a unique output value to each input value within its domain. In simpler terms, it’s a rule that tells us how to transform one set of values into another. Functions are ubiquitous in mathematics and science, describing everything from the motion of planets to the growth of bacteria.

To uncover the secrets of our enigmatic table, we must first identify the independent variable, often denoted by ‘x’, and the dependent variable, usually represented by ‘y’. The independent variable is the input value that we plug into the function, while the dependent variable is the output value that we get out. By carefully examining the pattern in the table, we can deduce the function that generated those values.

Once we have identified the function, we can evaluate it at any given input value. For instance, if our function is f(x) = 2x + 1, and we want to find f(5), we simply substitute 5 for x in the equation: f(5) = 2(5) + 1 = 11. Thus, the value of f(5) is 11.

In conclusion, deciphering the table represents a function, and finding the value of f(5) is a captivating intellectual pursuit that demands a blend of analytical thinking and mathematical prowess. By understanding the concept of functions, identifying the independent and dependent variables, and carefully examining the patterns in the table, we can unveil the hidden function and unveil its secrets. Embark on this mathematical odyssey and discover the wonders that functions hold.

## The Function Represented by a Table

A function is a relation between a set of inputs and a set of outputs, with the property that each input is associated with exactly one output. In other words, a function takes an input value and produces a corresponding output value.

A table of values for a function is a list of input-output pairs that represent the function. The table can be used to graph the function by plotting the input values on the x-axis and the output values on the y-axis.

**Example**

Consider the following table of values for a function:

| Input | Output |

|—|—|

| 1 | 2 |

| 2 | 4 |

| 3 | 6 |

| 4 | 8 |

| 5 | 10 |

This table represents the function f(x) = 2x. To find the output value for a given input value, simply multiply the input value by 2. For example, f(3) = 2 * 3 = 6.

### Determining the Function from a Table

To determine the function represented by a table of values, look for a pattern in the output values. In the example above, the output values are all even numbers that are twice the corresponding input values. This suggests that the function is f(x) = 2x.

However, it is important to note that not all functions can be determined from a table of values. For example, the following table of values could represent a variety of different functions:

| Input | Output |

|—|—|

| 1 | 2 |

| 2 | 3 |

| 3 | 5 |

| 4 | 7 |

| 5 | 11 |

Without more information, it is impossible to say what function is represented by this table.

## Finding f(5)

To find f(5), simply look up the output value for the input value of 5 in the table of values. In the example above, the output value for 5 is 10. Therefore, f(5) = 10.

### Variations

There are a number of different ways to represent a function. In addition to tables of values, functions can also be represented using graphs, equations, and verbal descriptions.

**Graphs**

A graph of a function is a visual representation of the function. The x-axis of the graph represents the input values, and the y-axis represents the output values. The graph of a function can be used to visualize the relationship between the input and output values.

**Equations**

An equation is a mathematical expression that represents a function. The equation of a function can be used to calculate the output value for a given input value.

**Verbal Descriptions**

A verbal description of a function is a written explanation of the function. The verbal description can include information about the domain and range of the function, as well as the relationship between the input and output values.

## Conclusion

The table represents a function f(x) = 2x. The value of f(5) is 10. Functions can be represented using tables of values, graphs, equations, and verbal descriptions.

### Frequently Asked Questions

**1. What is the domain of the function represented by the table?**

The domain of the function is the set of all possible input values. In the example above, the domain is the set of all real numbers.

**2. What is the range of the function represented by the table?**

The range of the function is the set of all possible output values. In the example above, the range is the set of all even numbers.

**3. Is the function represented by the table one-to-one?**

A function is one-to-one if each input value is associated with a unique output value. In the example above, the function is one-to-one because each input value is associated with a unique output value.

**4. Is the function represented by the table onto?**

A function is onto if every output value is associated with at least one input value. In the example above, the function is not onto because the output value of 1 is not associated with any input value.

**5. What is the inverse of the function represented by the table?**

The inverse of a function is a function that undoes the original function. The inverse of the function represented by the table is f^-1(x) = x/2.

.

Table,Represents,Function,What