129k views
3 votes
State the Equation and the Domain and Range for the Absolute Value Graph given (Use lowercase T to make the absolute value. Do not use spaces in your equation) у Equation: f(x)= 1]X-2 +3

1 Answer

3 votes

Final Answer:

The equation for the absolute value graph is
\( f(x) = |x - 2| + 3 \), and the domain is all real numbers
(\( x \in \mathbb{R} \)). The range is
\( f(x) \geq 3 \) since the absolute value of any real number is non-negative, and adding 3 ensures that the range starts from 3.

Step-by-step explanation:

The given equation
\( f(x) = |x - 2| + 3 \) represents an absolute value function where the expression
\( |x - 2| \) ensures that the function takes the absolute value of ( x - 2 ). This absolute value function shifts the graph horizontally by 2 units to the right.

For the domain, since
\( |x - 2| \) is valid for all real numbers, the domain of
\( f(x) \) is also all real numbers (\( x \in \mathbb{R} \)).

The range is determined by the absolute value part, which is always non-negative. Adding 3 to this ensures that the lowest value the function can take is 3. Therefore, the range is
\( f(x) \geq 3 \).

In summary, the equation
\( f(x) = |x - 2| + 3 \) describes an absolute value graph that is defined for all real numbers, and its range starts from 3 and goes upward.

User EricM
by
7.6k 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