Answer :
Let's tackle the problem by evaluating the given function [tex]\( D(F) = 2F + 115 \)[/tex] for the specified temperatures. We'll find the expression's value for each temperature, verify the values given, and use that information to determine the domain of the function from the provided options.
1. Calculate [tex]\( D(0) \)[/tex]:
Substitute [tex]\( F = 0 \)[/tex] into the function:
[tex]\[
D(0) = 2 \times 0 + 115 = 115
\][/tex]
2. Calculate [tex]\( D(-30) \)[/tex]:
Substitute [tex]\( F = -30 \)[/tex] into the function:
[tex]\[
D(-30) = 2 \times (-30) + 115 = -60 + 115 = 55
\][/tex]
3. Calculate [tex]\( D(11) \)[/tex]:
Substitute [tex]\( F = 11 \)[/tex] into the function:
[tex]\[
D(11) = 2 \times 11 + 115 = 22 + 115 = 137
\][/tex]
4. Calculate [tex]\( D(16) \)[/tex]:
Substitute [tex]\( F = 16 \)[/tex] into the function:
[tex]\[
D(16) = 2 \times 16 + 115 = 32 + 115 = 147
\][/tex]
Next, let's discuss the domain of the function based on what is physically reasonable. The question provides choices for the domain:
- A: [tex]\([-57.5^\circ, 32^\circ]\)[/tex]
- B: [tex]\([0^\circ, 41^\circ]\)[/tex]
- C: [tex]\([-15^\circ, 32^\circ]\)[/tex]
- D: [tex]\([-32^\circ, 115^\circ]\)[/tex]
Considering real-world conditions where temperatures are relevant for glare ice, the function should cover colder temperatures, possibly even below freezing, as they are critical for icy conditions. Given this context, choice D [tex]\([-32^\circ, 115^\circ]\)[/tex] allows for a reasonable range of cold temperatures on glare ice.
Therefore, option D is the most likely correct domain.
1. Calculate [tex]\( D(0) \)[/tex]:
Substitute [tex]\( F = 0 \)[/tex] into the function:
[tex]\[
D(0) = 2 \times 0 + 115 = 115
\][/tex]
2. Calculate [tex]\( D(-30) \)[/tex]:
Substitute [tex]\( F = -30 \)[/tex] into the function:
[tex]\[
D(-30) = 2 \times (-30) + 115 = -60 + 115 = 55
\][/tex]
3. Calculate [tex]\( D(11) \)[/tex]:
Substitute [tex]\( F = 11 \)[/tex] into the function:
[tex]\[
D(11) = 2 \times 11 + 115 = 22 + 115 = 137
\][/tex]
4. Calculate [tex]\( D(16) \)[/tex]:
Substitute [tex]\( F = 16 \)[/tex] into the function:
[tex]\[
D(16) = 2 \times 16 + 115 = 32 + 115 = 147
\][/tex]
Next, let's discuss the domain of the function based on what is physically reasonable. The question provides choices for the domain:
- A: [tex]\([-57.5^\circ, 32^\circ]\)[/tex]
- B: [tex]\([0^\circ, 41^\circ]\)[/tex]
- C: [tex]\([-15^\circ, 32^\circ]\)[/tex]
- D: [tex]\([-32^\circ, 115^\circ]\)[/tex]
Considering real-world conditions where temperatures are relevant for glare ice, the function should cover colder temperatures, possibly even below freezing, as they are critical for icy conditions. Given this context, choice D [tex]\([-32^\circ, 115^\circ]\)[/tex] allows for a reasonable range of cold temperatures on glare ice.
Therefore, option D is the most likely correct domain.
