Question

what does this transformation say to do?
(x, y) → (x, y + 4)

Explanation:

Step1: Analyze the transformation rule

The transformation is \((x,y)\to(x,y + 4)\). In a coordinate - plane, for a point \((x,y)\), when we change it to \((x,y + k)\) (where \(k\) is a non - zero constant):

• The \(x\) - coordinate remains the same. This means there is no horizontal shift (no left or right movement).
• The \(y\) - coordinate is increased by 4. In the context of vertical shifts in the coordinate plane, if \(y=f(x)\) is a function and we consider a point \((x,y)\) on its graph, changing the point to \((x,y + 4)\) is equivalent to moving the point 4 units in the positive \(y\) - direction.

Answer:

The transformation \((x,y)\to(x,y + 4)\) means to slide up 4.