Example 16 from Algebra and Trigonometry, 3.5 Transformation of Functions

Graphing a Horizontal Compression

Suppose a scientist is comparing a population of fruit flies to a population that progresses through its lifespan twice as fast as the original population. In other words, this new population, $R,$ will progress in 1 hour the same amount as the original population does in 2 hours, and in 2 hours, it will progress as much as the original population does in 4 hours. Sketch a graph of this population.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Symbolically, we could write

$\begin{matrix} R (1) & = & P (2), \\ R (2) & = & P (4), and in general, \\ R (t) & = & P (2 t) . \end{matrix}$
See Figure 24 for a graphical comparison of the original population and the compressed population.

Figure 24 (a) Original population graph (b) Compressed population graph

How did it go?

Solution

Solution