Which statement correctly characterizes an absolute value function in the form f(x) = |x - h| + k?

Which statement correctly characterizes an absolute value function in the form f(x) = |x - h| + k?

• A. The graph is shaped like a V and the domain is all real numbers
• B. The graph is shaped like a V and the domain is nonreal numbers
• C. The graph is shaped like a V and the domain is all real numbers
• D. The graph is a vertical line

Answer: (C)

An absolute value function like f(x) = |x - h| + k always makes a V-shaped graph that opens upward, with its vertex at the point (h, k) and the axis of symmetry x = h. The reason is that the expression inside the absolute value measures distance from x to h, so as x moves away from h in either direction, the output increases at the same rate. Because |x - h| is defined for every real x, adding k just shifts the whole graph up or down without restricting x, so the domain is all real numbers. It’s not a vertical line, and the domain isn’t restricted to nonreal numbers. So the description of a V-shaped graph with domain all real numbers accurately characterizes this function.

An absolute value function like f(x) = |x - h| + k always makes a V-shaped graph that opens upward, with its vertex at the point (h, k) and the axis of symmetry x = h. The reason is that the expression inside the absolute value measures distance from x to h, so as x moves away from h in either direction, the output increases at the same rate. Because |x - h| is defined for every real x, adding k just shifts the whole graph up or down without restricting x, so the domain is all real numbers. It’s not a vertical line, and the domain isn’t restricted to nonreal numbers. So the description of a V-shaped graph with domain all real numbers accurately characterizes this function.