Question

Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function f(x)= |x|y = |x-5|-1

Answer 1

Answer:

• Vertex: (5, –1)

,

• No symmetry

,

• Transformations: 5 units to the right, and 1 unit down.

Explanation

We are given the parent function f(x)= |x| and the transformed function:

$y=|x-5|-1$

Thus, we can get the vertex considering that a function in the form:

$y=|x\pm a|\pm b$

has a vertex at (+a, ±b).

Therefore, our vertex is at (5, –1). Additionally, as an absolute function has the form of a 'v', and as the vertex is at (5, –1) then it has no symmetry about the x-axis, nor y-axis, and nor about the origin, meaning it has no symmetry.

Finally, the transformation from the parent function is a shift 5 units to the right and one unit down.