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2.2 Your <strong>Notes</strong> linear Functions and Function notation Goal p Identify, evaluate, and graph linear functions. Vocabulary Linear function A function that can be written in the form y 5 mx 1 b where m and b are constants Function notation Using f(x) to represent the dependent variable of a function Example 1 Identify a Linear Function Tell whether the function is linear. Explain. a. f(x) 5 2x3 1 6 2 x b. g(x) 5 9 1 4x a. f is not a linear function because it has an x 3-term . b. g is a linear function because it can be rewritten as g(x) 5 4x 1 9 , so m 5 4 and b 5 9 . Checkpoint Tell whether the function is linear. Explain. 1. f(x) 5 6x 1 10 Yes; it is of the form y 5 mx 1 b. Example 2 Evaluate a Function Evaluate the function when x 5 3. 2. g(x) 5 2x2 1 4x 2 1 No; it is not of the form y 5 mx 1 b. a. f(x) 5 22x 1 5 b. g(x) 5 x2 2 x 2 1 a. f (x) 5 22x 1 5 Write original function. f ( 3 ) 5 22( 3 ) 1 5 Substitute 3 for x. 5 26 1 5 Multiply. 5 21 Simplify. 28 Lesson 2.2 • Algebra 2 C&S Notetaking Guide Copyright © McDougal Littell/Houghton Mifflin Company
Your <strong>Notes</strong> Homework b. g (x) 5 x 2 2 x 2 1 Write original function. g( 3 ) 5 ( 3 ) 2 2 3 2 1 Substitute 3 for x. 5 9 2 3 2 1 Multiply. 5 5 Simplify. Checkpoint Evaluate the function when x 5 24. 3. f(x) 5 2x 2 3 4. g(x) 5 2x 2 1 3x 211 20 Example 3 Graph a Linear Function Graph f(x) 5 2x 1 2. Solution Rewrite the function as y 5 2x 1 2. Find a point on the graph by substituting a convenient value for x . y 5 2x 1 2 Write equation. y y 5 2( 0 ) 1 2 Substitute 0 for x. y 5 2 Simplify. 1 O 1 One point is (0, 2) . Find a second point. y 5 2(1) 1 2 Substitute 1 for x . y 5 1 Simplify. A second point is (1, 1) . Draw a line through the two points. Checkpoint Complete the following exercise. 5. Graph h(x) 5 22x 1 1. Copyright © McDougal Littell/Houghton Mifflin Company Lesson 2.2 • Algebra 2 C&S Notetaking Guide 29 1 O y 1 x x
Page 1 and 2: 2.1 Your Notes Functions and Their
Page 3: Your Notes Homework GraphinG EquaTi
Page 7 and 8: Your Notes Example 2 Classify Lines
Page 9 and 10: Your Notes 2.4 quick Graphs of line
Page 11 and 12: Your Notes Example 2 Draw Quick Gra
Page 13 and 14: Your Notes 2.5 writing Equations of
Page 15 and 16: Your Notes Homework y 2 y 1 5 m(x 2
Page 17 and 18: Your Notes The value of k is called
Page 19 and 20: 2.7 Your Notes Scatter plots and co
Page 21 and 22: Your Notes Homework Example 3 Use a
Page 23: Point-slope form y 2 1 5 2(x 2 5) C

Notes with answers - Summit Schools

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