This document contains notes from a pre-calculus class that discuss finding the range of functions algebraically. It includes examples of finding the range of quadratic, rational, logarithmic, and exponential functions. It emphasizes looking at restrictions on y values before determining the inverse of a function to find its range. Students are assigned to complete a domain and range worksheet and have a quiz on this material.

1. Warm-UpWarm-Up

2. Homework QuestionsHomework Questions

3. Range AlgebraicallyRange Algebraically
Pre-CalculusPre-Calculus
Mrs. RamseyMrs. Ramsey

4. Find the RangeFind the Range


2
y x=
2
4y x= −

5. Find the RangeFind the Range


2
( 2)y x= −
2
( 3) 7y x= − +

6. Rational ProblemsRational Problems
 1
y
x
=
3
2
x
y
x
+
=
−

7. Rational ProblemsRational Problems
 3
5y x= + 5
6 1y x= − −

8. Log ProblemsLog Problems
  log( 3)y x= +ln( 6)y x= +

9. Exponential ProblemsExponential Problems
 
2x
y = ( 4)
3 1x
y −
= +

10. Find the RangeFind the Range


2
6 1y x x= + −
2
4 9y x x= − −

11. Find the Range = need to look at restrictionsFind the Range = need to look at restrictions
on y before we find inverseon y before we find inverse

 2
4y x= −
8y x= −

12. Find the RangeFind the Range


2 6y x= + −
4 1y x= − − +

13. Find the domain and rangeFind the domain and range

2
1
9
y
x
=
−

14. HomeworkHomework
 QUIZQUIZ
 Domain and Range WorksheetDomain and Range Worksheet