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 Domain explained

 Domain - Set of values that an independent variable of a function can have.

 function  y=2x. x is an independent variable that can have and is the domain.

 If  y=2x^2 + x so what is the domain? Domain name An identification string.

Sure, let's illustrate the domain of the given functions in R programming code.

For the first function \(y = 2x\), where \(x\) is the independent variable, the domain includes all real numbers. Here's how you can represent it in R:

```R

# Function y = 2x

domain_function1 <- function(x) {

  y <- 2 * x

  return(y)

}

# Example usage

x_values <- seq(-10, 10, by = 1)

y_values_function1 <- domain_function1(x_values)

# Display the results

data.frame(x = x_values, y = y_values_function1)

```

For the second function \(y = 2x^2 + x\), the domain is still all real numbers because there are no restrictions on the values that \(x\) can take. Here's the R code for the second function:

```R

# Function y = 2x^2 + x

domain_function2 <- function(x) {

  y <- 2 * x^2 + x

  return(y)

}

# Example usage

y_values_function2 <- domain_function2(x_values)

# Display the results

data.frame(x = x_values, y = y_values_function2)

```

In both cases, you can see that we use the `seq` function to generate a sequence of \(x\) values, and then we calculate the corresponding \(y\) values using the defined functions. The resulting data frames show the pairs of \(x\) and \(y\) values, illustrating the domain of the functions.

How are domain and domain names related? A variable can be used inside a string. There are string variables. 

What is the public domain?

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