9. Compare the function with the parent function. Without graphing, what are the
vertex, axis of symmetry, and transformations of the given function?
y = |6x + 3| − 1
The parent function for this given function is y = |x|.
The vertex of the given function is the point (-3/6, -1), which is found by setting the expression inside the absolute value equal to zero: 6x + 3 = 0, and solving for x.
The axis of symmetry is the vertical line that passes through the vertex, which is the line x = -3/6.
The transformations of the given function are as follows:
1. The graph is shifted 3/6 units to the left from the parent function.
2. The graph is shifted 1 unit downward from the parent function.
These transformations cause the vertex and axis of symmetry of the given function to differ from that of the parent function.