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Livia eats a chicken drumstick with 11 grams of protein. She also eats [tex]\( x \)[/tex] cheese sticks, each with 7 grams of protein. The table shows [tex]\( y \)[/tex], the total number of grams of protein that Livia will consume if she eats [tex]\( x \)[/tex] cheese sticks. Livia may eat only part of a cheese stick, so [tex]\( x \)[/tex] may not always be a whole number.

[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
0 & 11 \\
\hline
2.5 & 28.5 \\
\hline
5 & 46 \\
\hline
7 & 60 \\
\hline
\end{tabular}
\][/tex]

What is the range of the function?

A. all real numbers

B. all real numbers greater than or equal to 0

C. all real numbers greater than or equal to 11

D. all integers greater than or equal to 11

Sagot :

GinnyAnswer
To determine the range of the function, we need to analyze the total number of grams of protein [tex]\( y \)[/tex] that Livia consumes based on the number of cheese sticks [tex]\( x \)[/tex] she eats.

Let's break down the given information step by step:

1. Chicken Drumstick Protein: The protein from the chicken drumstick is always 11 grams, which is a constant value.

2. Cheese Stick Protein: Each cheese stick contains 7 grams of protein. Therefore, if Livia eats [tex]\( x \)[/tex] cheese sticks, the protein from cheese sticks would be [tex]\( 7x \)[/tex] grams.

3. Total Protein: The total protein [tex]\( y \)[/tex] Livia consumes is the sum of the protein from the chicken drumstick and the cheese sticks. Mathematically, this can be expressed as:
[tex]\[ y = 11 + 7x \][/tex]

Now, let's use this relationship to determine the quantities in the table:

- For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 11 + 7(0) = 11 \text{ grams} \][/tex]

- For [tex]\( x = 2.5 \)[/tex]:
[tex]\[ y = 11 + 7(2.5) = 11 + 17.5 = 28.5 \text{ grams} \][/tex]

- For [tex]\( x = 5 \)[/tex]:
[tex]\[ y = 11 + 7(5) = 11 + 35 = 46 \text{ grams} \][/tex]

- For [tex]\( x = 7 \)[/tex]:
[tex]\[ y = 11 + 7(7) = 11 + 49 = 60 \text{ grams} \][/tex]

These values match the values given in the table:

[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 0 & 11 \\ \hline 2.5 & 28.5 \\ \hline 5 & 46 \\ \hline 7 & 60 \\ \hline \end{tabular} \][/tex]

Considering the formula [tex]\( y = 11 + 7x \)[/tex], and knowing that [tex]\( x \)[/tex] can be any non-negative real number (since Livia can eat parts of cheese sticks), we see that:

- When [tex]\( x = 0 \)[/tex], the minimum value of [tex]\( y \)[/tex] is 11 grams.
- As [tex]\( x \)[/tex] increases, [tex]\( y \)[/tex] will continue to increase linearly.

Thus, the smallest value [tex]\( y \)[/tex] can take is 11 grams when [tex]\( x = 0 \)[/tex]. There is no upper limit for [tex]\( y \)[/tex] because [tex]\( x \)[/tex] can grow indefinitely large.

Therefore, the range of [tex]\( y \)[/tex] is:

[tex]\[ \text{All real numbers greater than or equal to 11} \][/tex]

This matches the option: all real numbers greater than or equal to 11.
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