1. Solve the equation. Check your solution. 𝑥 𝑥+3 + 9 𝑥−2 = 27 𝑥 2 +𝑥−6
Problem of the Day

2. Section 8-3 Graphing Reciprocal Functions

3. Then Now Objectives You graphed polynomial functions.
Determine properties of reciprocal functions.
Graph transformations of reciprocal functions.

4. Common Core State Standards
Content Standards
A.CED.2 – Create equations in two or more variable to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
F.BF.3 – Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k; find the value of k given the graphs.
Mathematical Practices
2) Reason abstractly and quantitatively.
Common Core State Standards

5. Reciprocal Function: has an equation of the form 𝑓 𝑥 = 1 𝑎(𝑥) , where a(x) is a linear function and a(x) ≠ 0.
Vocabulary

6. Parent Function of Reciprocal Functions

7. Determine the value of x for which 𝑓 𝑥 = 2 𝑥−1 is not defined.
Example 1

8. Determine the value of x for which each function is not defined
Example 1

9. The graphs of reciprocal functions may have breaks in continuity for excluded values. Some may have an asymptote, which is a line that the graph of the function approaches.
Vocabulary

10. Identify the asymptotes, domain, and range of the function.
Example 2

11. Identify the asymptotes, domain, and range of the function.
Example 2

12. Identify the asymptotes, domain, and range of each function.
Example 2

13. Transformations of Reciprocal Functions

14. Graph the function: f(x) = − 1 𝑥 − 3 – 4 Give the necessary information for the function. Vert. Asym: ________________ Horiz. Asym: _______________ Domain: __________________ Range: ____________________
Example 3

15. Graph the function: f(x) = − 1 𝑥 Give the necessary information for the function. Vert. Asym: ________________ Horiz. Asym: _______________ Domain: __________________ Range: ____________________
Example 3

16. Graph the function: f(x) = 3 𝑥 − Give the necessary information for the function. Vert. Asym: ________________ Horiz. Asym: _______________ Domain: __________________ Range: ____________________
Example 3

17. p.548 #1, 2, 7 – 10, 18, 19
Homework