Question

Consider the equation y = |x|. What effect will replacing x with x + 7 have on the graph?

a) The axis of symmetry will shift 7 units.
b) It will no longer have an x-intercept.
c) The y-intercept will shift 7 units.
d) The vertex will shift 7 units.

Answer 1

Replacing x with x + 7 in the equation y = |x| shifts the axis of symmetry and the vertex of the graph 7 units to the left.

Step-by-step explanation:

When considering the equation y = |x| and the effect of replacing x with x + 7, it's essential to understand the properties of absolute value functions and transformations. The graph of y = |x| is a V-shaped graph with its vertex at the origin (0,0) and an axis of symmetry along the y-axis. When we replace x with x + 7, the new equation becomes y = |x + 7|. This transformation effectively shifts the entire graph to the left by 7 units. The axis of symmetry will shift 7 units to the left, and similarly, the vertex of the graph will shift 7 units to the left. These shifts correspond to a horizontal transformation of the function.