Answer:
C) Vertex (-4, 0), Range: {y | 0 ≤ y < ∞}
Step-by-step explanation:
The given table represents an absolute value function f(x):
[tex]\begin{array}{|l|c|c|c|c|c|c|c|c|c|}\cline{1-10}x&-5&-4&-3&-2&-1&0&1&2&3\\\cline{1-10}f(x)&1&0&1&2&3&4&5&6&7\\\cline{1-10}\end{array}[/tex]
Vertex
The vertex of an absolute value function is the point where the graph changes direction. It represents either the minimum or maximum point, depending on whether the graph opens upwards or downwards.
From examining the given table, it appears that the absolute value function opens upwards, as the values of f(x) increase as x moves away from -4 in both directions. Therefore, the vertex represents the minimum point of the function.
The minimum value of the function is f(x) = 0, which occurs at x = -4. So, the vertex of the function is:
[tex]\Large\boxed{\boxed{\textsf{Vertex:}\;(-4, 0)}}[/tex]
Range
The range of a function is the set of all possible output values.
For an upward-opening absolute value function, the range consists of all real numbers greater than or equal to the y-coordinate of the vertex. This is because the function increases without bound as x moves away from the vertex.
The y-coordinate of the vertex is y = 0. Therefore, the range is:
[tex]\Large\boxed{\boxed{\textsf{Range:}\;\{y \;| \;0 \leq y < \infty\} }}[/tex]
