To determine the range of the function, let's analyze the protein consumption scenario step-by-step.
1. Understanding the Components: Livia always eats a chicken drumstick which provides her with a fixed amount of protein, specifically 11 grams. This is a constant contribution to her protein intake.
2. Contribution from Cheese Sticks: In addition to the chicken drumstick, she eats [tex]\( x \)[/tex] cheese sticks. Each cheese stick contains 7 grams of protein. The quantity [tex]\( x \)[/tex] represents the number of cheese sticks and it can be any real number (including fractional parts since she can eat part of a cheese stick).
3. Total Protein Intake Calculation: The total protein intake [tex]\( y \)[/tex] can be expressed as:
[tex]\[
y = 11 + 7x
\][/tex]
where:
- 11 grams come from the chicken drumstick,
- [tex]\( 7x \)[/tex] grams come from [tex]\( x \)[/tex] cheese sticks.
4. Establishing the Range of [tex]\( y \)[/tex]:
- The lowest possible value of [tex]\( x \)[/tex] is 0 (meaning no cheese sticks are eaten).
- For [tex]\( x = 0 \)[/tex], [tex]\( y = 11 + 7 \cdot 0 = 11 \)[/tex] grams.
- As [tex]\( x \)[/tex] can take on any real value including fractions and can increase indefinitely, [tex]\( y \)[/tex] will increase accordingly without any upper bound.
Thus, the function [tex]\( y = 11 + 7x \)[/tex] ranges from the minimum possible value of 11 (when [tex]\( x = 0 \)[/tex]) and can take any value greater than or equal to 11 as [tex]\( x \)[/tex] increases.
Hence, the range of the function [tex]\( y \)[/tex] is:
[tex]\[
\text{all real numbers greater than or equal to 11}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\text{all real numbers greater than or equal to 11}}
\][/tex]
