Question

What is the axis of symmetry of the function y = |x - 6| - 3?

A) x = -3
B) x = 3
C) x = 6
D) x = 9

Answer 1

The axis of symmetry for the function y = |x - 6| - 3 is the vertical line x = 6, which is option C.

Step-by-step explanation:

The axis of symmetry for the function y = |x - 6| - 3 is found by looking at the expression within the absolute value bars. For an absolute value function of the form y = |x - h|, the axis of symmetry is x = h. Here, h is the value that makes the expression within the absolute value zero, because the graph is mirrored across this line. In the given function, the expression within the absolute value is (x - 6), which is equal to zero when x is 6. Therefore, the axis of symmetry for the function y = |x - 6| - 3 is the vertical line x = 6.