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 given function is a absolute value function, which can be described as f(x) = |x|. The parent function, f(x) = |x|, has a vertex at the origin (0, 0) and its axis of symmetry is the y-axis (x = 0).
For the given function, y = |6x - 2| - 7, the vertex and axis of symmetry can be found by setting the expression inside the absolute value equal to zero:
6x - 2 = 0
6x = 2
x = 2/6
x = 1/3
So the vertex is (1/3, -7) and the axis of symmetry is x = 1/3.
Next, let's analyze the transformations. The expression inside the absolute value, 6x - 2, is multiplied by 6 which indicates a vertical stretching or compression. In this case, the graph is compressed vertically by a factor of 1/6.
Finally, the graph is shifted downwards by 7 units (y - 7).