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Introduction to Linear Relations and Functions Do Now: The following table contains measurement of temperature in Celsius ( C ) and Fahrenheit ( F ). C F= 0 32 5 41 10 50 15 59 20 68 1. Plot the given data from the chart. 2. Based on the scatter plot sketched above, describe the relation between C and F. 3. Write an equation to express relation C and F. 25 77 Definition of a Linear Function Examples of linear functions General graphs of linear functions ( special lines – vertical and horizontal lines ) Domain and Range Definition of function Definition of a one–to–one function Notation of functions f ( x) 2 x 3 g (a ) .5a 5 2 1 h( k ) k 5 2 Note: f(x), g(a), and h(k) are called the dependent variables whose independent variables are x, a, and k respectively. Inverse of linear functions 1. Algebraic definition: 2. Graphic definition: 3. Examples of inverse notation: f 1 x y 1 g 1 x Class work 1. Determine whether each of following is a linear function. a. f ( x) 3x 4 b. g ( x) x 3 5 d . h( x ) x 2 3 x e. f ( x) 6 f. c. y x 6 y x 5 g. x 6 2. Complete the table below. Equations y Domain Range Is it a functions Is it a oneto-one function 2 x6 3 f x 2( x 2) g ( x ) 3 x2 3. Write an equation of the inverse for each. a ) y 5 x 3 b) f ( x ) 1 x 3 2 c) 2 x y 6 4. Write the equation of the line passing through points ( -5, 2 ), ( 4, 10 ). Is the inverse a function Homework 1. Determine whether each of following is a linear function. a. f ( x) .2 x 5 d . h( x ) 1 2 x 8x 2 b. x 5 e. 3 y 7 2 x x 2 x f. 4 y c. y g . y 2 2. Complete the following table. Equations y Domain Range Is it a functions Is it a oneto-one function 1 x2 5 f x 5 g ( x) x 6 x 5 3. Write the equation of the inverse for each. a) y 7 x 2 b) x 3 y 9 c) f ( x) 2 x 5 3 4. Write the equation of the line passing through points ( 3, 0 ), ( -1, 6 ). Is the inverse a function