Question

On a coordinate plane, an absolute value graph has a vertex on the x-axis in the first quadrant.
Which functions could be represented by the graph? Check all that apply.

f(x) = | x + 0.14|
f(x) = |x| + 1.3
f(x) = |x – 7|
f(x) = |x + 12|
f(x) = |x| – 17
f(x) = |x – 23|

Answer 1

A vertex on the x-axis in the first quadrant means the vertex is at (h,0) with h>0. The vertex of |x - a| is (a,0), and of |x + b| is (-b,0); vertical shifts move the y-coordinate off 0.

Thus the functions with vertices at (positive,0) are:
- f(x) = |x − 7|
- f(x) = |x − 23|