Question

f(x) = - |x| + 4 In complete sentences to answer the following prompts. A. Define the key features of the graph of the provided absolute value function. B. Provide the coordinate of the vertex and two additional points on the graph. C. Use the coordinate of the function’s vertex to prove the domain and range of the function.

Answer 1

A. The absolute function is negative since the negative sign outside of |x| reflects the function downward. The +4 translates the absolute value function up 4 units, making the vertex be at (0,4) instead of the origin.

B. The vertex is at (0,4), and two other points are (5,-1) and (-1,3).

C. Since the vertex of the function is (0,4), the range of the function can only go from -∞ to 4; the range is (-∞,4]. The domain is still all real numbers, so it is still (-∞,∞).

Explanation: