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

Section 8-3 Graphing Reciprocal Functions

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

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

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

Parent Function of Reciprocal Functions

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

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

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

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

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

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

Transformations of Reciprocal Functions

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

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

Graph the function: f(x) = 3 𝑥 − 2 + 4 Give the necessary information for the function. Vert. Asym: ________________ Horiz. Asym: _______________ Domain: __________________ Range: ____________________ Example 3

p.548 #1, 2, 7 – 10, 18, 19 Homework