Question

Question was provided via image upload.

Explanation:

Identify the parent function and its range

Using the Absolute Value Functions and Range of Functions knowledge points

$$
LATEXBLOCK0
$$

Apply the translations to the function

Using the Function Translations knowledge point

$$
LATEXBLOCK1
$$

Determine the range of the translated function

Using the Range of Functions and Absolute Value Functions knowledge points

$$
LATEXBLOCK2
$$

Compare the ranges of both functions

Using the Range of Functions knowledge point

$$
LATEXBLOCK3
$$

Answer:

• The range is the same for both functions: \(\{y \mid y \text{ is a real number}\}\)
• The range is the same for both functions: \(\{y \mid y \ge 0\}\)
• The range changes from \(\{y \mid y \ge 0\}\) to \(\{y \mid y \ge 2\}\) (Correct answer)
• The range changes from \(\{y \mid y \ge 0\}\) to \(\{y \mid y \ge 6\}\)