Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformations of the given function? y = │6x – 2│ – 7
The parent function of the given function is y = |x|.
The given function y = |6x – 2| – 7 has a transformation of the parent function. The constant inside the absolute value function, 6, stretches the parent function horizontally by a factor of 1/6. The constant outside the absolute value function, -7, shifts the parent function downward by 7 units.
To find the vertex and axis of symmetry of the given function, we need to find the x-value that makes the expression inside the absolute value function equal to zero.
6x - 2 = 0
6x = 2
x = 2/6
x = 1/3
Therefore, the vertex is (1/3, -7) and the axis of symmetry is x = 1/3.