161k views
5 votes
What are the domain and range of f(x) = (x - 3)| + 6?

Option 1: Domain: x is all real numbers, Range: y
Option 2: Domain: x > 3, Range: y > 6
Option 3: Domain: x is all real numbers, Range: y
Option 4: Domain: x , Range: y > -6

User Chitza
by
8.6k points

1 Answer

6 votes

Final answer:

The correct option for the domain and range of the given function f(x) = (x - 3) with an absolute value sign and plus 6 is Option 1, which states that the domain is all real numbers and the range is all numbers greater than or equal to 6.

Step-by-step explanation:

The function provided f(x) = (x - 3) with an absolute value sign around (x - 3) and plus 6 at the end is a transformation of the basic absolute value function. The absolute value function by itself, which is |x|, can take any real number as an input, meaning its domain is all real numbers. In this case, the subtraction of 3 inside the absolute value does not change the domain, because we can still input any real number and get a result. The addition of 6 on the outside shifts the graph upwards, but it also does not affect the domain.

For the range, since absolute values are always non-negative and we are adding 6 to it, the smallest value f(x) can take is when x is 3. At x = 3, (x-3) becomes zero, so f(x) becomes |0| + 6, which is 6. Therefore, the function can never be less than 6, making the range y ≥ 6.

With this in mind, Option 1 is correct: Domain: x , Range: y .

User GuerillaNerd
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories