Here are 4 equations defining 4 different functions, and . List them in order of increasing rate of change. That is, start with the one that grows the slowest and end with the one that grows the quickest.

Technology required. Function  is defined by , and function  is defined by .

Functions and are given by and . As increases from 0:

1. Which function reaches 30 first?
2. Which function reaches 100 first?

The functions  and  are defined by and .

1. Which function eventually grows faster,  or ? Explain how you know.
2. Explain why the graphs of and meet for a positive value of .

A line segment of length is scaled by a factor of 1.5 to produce a segment with length . The new segment is then scaled by a factor of 1.5 to give a segment of length .

What scale factor takes the segment of length  to the segment of length ? Explain your reasoning.

A couple needs to get a loan of $5,000 and has to choose between three options.

• Option A: applied quarterly
• Option B: applied every 4 months
• Option C: applied semi-annually

If they make no payments for 5 years, which option will give them the least amount owed after 5 years? Use a mathematical model for each option to explain your choice.

Here are graphs of five absolute value functions. Match the graph and equation that represent the same function.