Splash Screen. CCSS Content Standards A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations.

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Splash Screen

CCSS Content Standards A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. F.BF.4a Solve an equation of the form f (x ) = c for a simple function f that has an inverse and write an expression for the inverse. Mathematical Practices 6 Attend to precision. Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Then/Now You represented relations as tables, graphs, and mappings. Find the inverse of a relation. Find the inverse of a linear function.

Vocabulary inverse relation inverse function

Example 1 Inverse Relations To find the inverse, exchange the coordinates of the ordered pairs. (–3, 26) → (26, –3) (6, –1) → (–1, 6) (2, 11) → (11, 2) (  1, 20) → (20,  1) A. Find the inverse of each relation. {(−3, 26), (2, 11), (6, −1), (−1, 20)} Answer: The inverse is {(26, –3), (11, 2), (–1, 6), (20, –1)}.

Example 1 Inverse Relations B. Find the inverse of each relation. Write the coordinates as ordered pairs. Then exchange the coordinates of each pair. (  4,  3) → (  3,  4) (–2, 0) → (0, –2) (1, 4.5) → (4.5, 1) (5, 10.5) → (10.5, 5) Answer: The inverse is {(3, 4), (4.5, 1), (0, –2), (10.5, 5)}.

Example 1 A.{(4, 8), (–6, 6), (3, 3), (0, –8)} B.{(8, 4), (6, –6), (3, 3), (–8, 0)} C.{(0, –8), (3, 3), (–6, 6), (4, 8)} D.{(–4, –8), (6, –6), (–3, –3), (0, 8)} Find the inverse of {(4, 8), (–6, 6), (3, 3), (0, –8)}.

Example 2 Graph Inverse Relations A. Graph the inverse of each relation.

Example 2 Answer: The graph of the relation passes through the points at (–2, 6), (2, 0), and (6, 6). To find points through which the graph of the inverse passes, exchange the coordinates of the ordered pairs. The graph of the inverse passes through the points at (6, –2), (0, 2), and (6, 6). Graph these points and then draw the line that passes through them. Graph Inverse Relations

Example 2 Graph Inverse Relations B. Graph the inverse of each relation.

Example 2 Answer: The graph of the relation passes through the points at (–2,– 6), (0, 4), (2, 0), (4, –4), and (6, –8). To find points through which the graph of the inverse passes, exchange the coordinates of the ordered pairs. The graph of the inverse passes through the points at (6, 2), (4, 0), (0, 2), (–4, 4), and (–8, 6). Graph these points and then draw the line that passes through them. Graph Inverse Relations

Example 3 Find Inverse Linear Functions A. Find the inverse of the function f (x) = –3x Step 1 f(x)= –3x + 27Original equation y= –3x + 27Replace f(x) with y. Step 2 x = –3y + 27Interchange y and x. Step 3 x – 27 = –3ySubtract 27 from each side. Divide each side by –3.

Example 3 Simplify. Step 4 Answer: The inverse of f(x) = –3x + 27 is Find Inverse Linear Functions

Example 3 Find Inverse Linear Functions

Example 3 Find the inverse of f(x) = 12 – 9x. A. B. C. D.