This document provides an overview of rational functions including how to simplify and determine intercepts, zeros, and asymptotes of rational functions. It gives examples of solving rational equations by finding the value of x. It also presents a word problem about the maximum depth a scuba diver can dive within 30 minutes without needing decompression stops on the way back up, as determined by the rational function T(d) = 1700/(d-33) relating dive time and depth.

2. OBJECTIVE
S
 Recall how to simplify rational
functions.
 Determine the intercepts, zeroes
and asymptotes of rational
function.
 Solve problems involving rational
functions.

3. RECALL

4. ASYMPTOTES

5. HORIZONTAL ASYMPTOTE

6. EXAMPLE 1

7. EXAMPLE 2

8. EXAMPLE 3

9. RATIONAL EQUATION

10. What is a rational equation?
A rational equation is an equation
containing at least one rational
expression. Rational expressions
typically contain a variable in the
denominator.

11. EXAMPLE 1
Find the value/s of x.
𝑥 +
8
𝑥
= 6

12. EXAMPLE 2
Find the value of x.
𝑥+3
𝑥−3
=
12
3

13. PROBLEM SOLVING
If a scuba diver goes to depth greater than 33 feet,
the function 𝑇 𝑑 =
1700
𝑑−33
gives the maximum time
a diver can remain down and still surface at a
steady rate with no decompression stops. In this
function, 𝑇(𝑑) represents the dive time in minutes,
and d represents the depth in feet. If a diver plans
a 30 – minute dive, what is the maximum depth
the diver can go without decompression stops on
the way back – up?