The range of the function 𝑓(𝑥)=|𝑥−2|+1 is 𝑦≥1.

Here's why:

1. The absolute value function |𝑥−2| is always greater than or equal to 0 because absolute value represents distance, which can't be negative.

2. When you add 1 to the absolute value function to get |𝑥−2|+1, you shift the entire graph up by 1 unit.

3. Therefore, the smallest value the function 𝑓(𝑥)=|𝑥−2|+1 can have is 1 (when 𝑥=2), and it can increase from there without bound.

So, the range is all real numbers greater than or equal to 1, or 𝑦≥1.

Question

The range of the function 𝑓(𝑥)=|𝑥−2|+1 is 𝑦≥1.

Here's why:

1. The absolute value function |𝑥−2| is always greater than or equal to 0 because absolute value represents distance, which can't be negative.

2. When you add 1 to the absolute value function to get |𝑥−2|+1, you shift the entire graph up by 1 unit.

3. Therefore, the smallest value the function 𝑓(𝑥)=|𝑥−2|+1 can have is 1 (when 𝑥=2), and it can increase from there without bound.

So, the range is all real numbers greater than or equal to 1, or 𝑦≥1.

Knowee AI · Accepted Answer

The range of the function 𝑓(𝑥)=|𝑥−2|+1 is 𝑦≥1.

Here's why:

1. The absolute value function |𝑥−2| is always greater than or equal to 0 because absolute value represents distance, which can't be negative.

2. When you add 1 to the absolute value function to get |𝑥−2|+1, you shift the entire graph up by 1 unit.

3. Therefore, the smallest value the function 𝑓(𝑥)=|𝑥−2|+1 can have is 1 (when 𝑥=2), and it can increase from there without bound.

So, the range is all real numbers greater than or equal to 1, or 𝑦≥1.

Describe the range of the following absolute value function:𝑓(𝑥)=|𝑥−2|+1𝑓(𝑥)=|𝑥−2|+1The range is: 𝑦