Question

Identify the key features of the function f(x) = |x - 31|.

A) Vertex, axis of symmetry, direction of opening, intercepts
B) Slope, y-intercept, vertex, axis of symmetry
C) Range, domain, intercepts, vertex
D) Direction of opening, vertex, range, domain

Answer 1

The function f(x) = |x - 31| has a vertex at (31, 0), an axis of symmetry at x = 31, opens upwards, and intercepts the x-axis at the vertex with no y-intercept. The correct answer is option A.

Step-by-step explanation:

The key features of the function f(x) = |x - 31| are as follows:

• Vertex: This is the point where the function changes direction. For the given function, the vertex is at (31, 0) because this is where the function's value is zero.
• Axis of symmetry: This is a vertical line that splits the graph into two mirror images. For the given function, the axis of symmetry is x = 31.
• Direction of opening: Since this is an absolute value function, it opens upwards. The branches of the graph move away from each other as x moves away from 31.
• Intercepts: The graph intercepts the x-axis at the vertex (31, 0). There is no y-intercept as the graph does not cross the y-axis.

Therefore, the correct answer is option A. These features help define the shape and position of the graph on the coordinate plane.