Let \(c\) be a positive real number. Vertical and horizontal shifts in the graph of \(y = f(x)\) are represented as follows:

1. Vertical shift \(c\) units upward:
   $$
   h(x) = f(x) + c
   $$
2. Vertical shift \(c\) units downward:
   $$
   h(x) = f(x) – c
   $$
3. Horizontal shift \(c\) units to the right:
   $$
   h(x) = f(x-c)
   $$
4. Horizontal shift \(c\) units to the left:
   $$
   h(x) = f(x+c)
   $$

Reflections in the coordinate axes of the graph of \(y = f(x)\) are represented as follows.

1. Reflection in the \(x\)-axis:
   $$
   h(x) = -f(x)
   $$
2. Reflection in the \(y\)-axis:
   $$
   h(x) = f(-x)
   $$

A vertical stretch of the graph \(y = f(x)\) is represented by \(g(x) = c f(x),\) where \(c>1\). A vertical shrink is represented by \(g(x) = c f(x),\) where \( 0 < c < 1\). A horizontal stretch is represented by \(g(x) = f(c x),\) where \(0 < c < 1\). A horizontal shrink is represented by \(g(x)= f(c x),\) where \(c > 1.\)