Final answer:
The vertex of the absolute value function f(x) = |x + 11| - 7 is at the point (-11, -7). The domain is all real numbers and the range is f(x) ≥ -7.
Step-by-step explanation:
The vertex of an absolute value function, which has a general form of f(x) = |ax + b| + c, occurs at the point where the expression inside the absolute value is zero. For the given function f(x) = |x + 11| - 7, we set the expression within the absolute value to zero and solve for x which gives us x = -11. Thus, the vertex is located at (-11, -7).
The domain of an absolute value function is the set of all real numbers, because there are no restrictions on the values that x can take. The range of this function is the set of all real numbers y such that f(x) ≥ -7, because the lowest point on the graph of the function is the vertex and the value of the function never decreases below the y-coordinate of the vertex (-7). Therefore, the function increases above -7 for all other x values.
So the correct domain and range for the function f(x) = |x + 11| - 7 are:
- Domain: All real numbers
- Range: f(x) ≥ -7
The correct answer to the student's question is:
The vertex is located at (-11, -7).
Identify the domain and range of the function:
A) Domain: All real numbers; Range: f(x) ≥ -7