Question

function v gives the absolute temperature error as a function of the room temperature in degrees celsius, x. select all statements that are true about the function and the situation. a when the room temperature is 0 degrees celsius, v(0) has a value of 2. b when the room temperature is -3 degrees celsius, the absolute temperature error, v(-3), is -1. c when the room temperature is 3 degrees celsius, v(3) is 5. d the equation v(x) = |x - 2| gives us the absolute temperature error when the room temperature is x degrees celsius. e when v(x) = 0.5, the room temperature could be -1.5 or -2.5 degrees celsius.

Explanation:

To solve this, we analyze each option using the function \( e(x) = |x - 2| \) (from option D, which we'll verify first).

Option A

Evaluate \( e(0) \):
\( e(0) = |0 - 2| = |-2| = 2 \).
This is true.

Option B

Evaluate \( e(-3) \):
\( e(-3) = |-3 - 2| = |-5| = 5 \), not \(-1\). Absolute value is non - negative, so this is false.

Option C

Evaluate \( e(3) \):
\( e(3) = |3 - 2| = |1| = 1 \), not \( 5 \). This is false.

Option D

The function \( e(x)=|x - 2| \) represents the absolute difference between the room temperature \( x \) and a target temperature (likely \( 2^\circ \text{C} \)), which is the definition of absolute temperature error. This is true.

Option E

Solve \( e(x)=0.5 \), so \( |x - 2| = 0.5 \).
Case 1: \( x - 2 = 0.5 \Rightarrow x = 2.5 \).
Case 2: \( x - 2=-0.5 \Rightarrow x = 1.5 \).
The proposed values (\(-1.5\) or \(-2.5\)) do not satisfy the equation. This is false.

Answer:

A. When the room temperature is 0 degrees Celsius, \( e(0) \) has a value of 2.
D. The equation \( e(x)=|x - 2| \) gives us the absolute temperature error when the room temperature is \( x \) degrees Celsius.