Let's determine the range of the function based on the given information.
1. Livia eats a chicken drumstick which contains 11 grams of protein. This is represented by [tex]\( y = 11 \)[/tex] when [tex]\( x = 0 \)[/tex].
2. Additionally, she eats [tex]\( x \)[/tex] cheese sticks, each containing 7 grams of protein.
3. The total grams of protein [tex]\( y \)[/tex] Livia consumes when she eats [tex]\( x \)[/tex] cheese sticks is therefore given by the function:
[tex]\[
y = 11 + 7x
\][/tex]
Now, let’s use the provided table to observe the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 11 \)[/tex]
- When [tex]\( x = 2.5 \)[/tex], [tex]\( y = 28.5 \)[/tex]
- When [tex]\( x = 5 \)[/tex], [tex]\( y = 46 \)[/tex]
- When [tex]\( x = 7 \)[/tex], [tex]\( y = 60 \)[/tex]
From the function [tex]\( y = 11 + 7x \)[/tex], we see that the total grams of protein [tex]\( y \)[/tex] increases as the number of cheese sticks [tex]\( x \)[/tex] increases.
Determining the range:
- The smallest value [tex]\( y \)[/tex] can take is 11 grams (when [tex]\( x = 0 \)[/tex]).
- Since [tex]\( x \)[/tex] can be any non-negative real number (including fractions, as Livia can eat part of a cheese stick), [tex]\( y \)[/tex] can be any value starting from 11 and increasing indefinitely.
Therefore, the range of the function is all real numbers greater than or equal to 11.
Hence, the correct answer is:
[tex]\[
\text{all real numbers greater than or equal to 11}
\][/tex]
