advertisement

Warm up What is the solution of : 1) 2𝑥 + 1 − 4 = 3𝑥 X = -1 Why is there only one answer? 2) Explain why the equation 7𝑥 + 2 = −11 has no solution. An absolute value will NEVER be negative. Unit 2 2-1 Relations and Functions Functions, Equations and Graphs Unit Objectives: • • • Identify and use different forms of linear equations Identify and use transformations on graphs and equations/functions Model real-life situations with linear functions. Today’s Objective: I can graph relations and identify functions. Relations: Mapping Diagram Input Output -3 3 4 4 -1 -1 3 a set of input and output values Table of values Ordered pairs (input, output) (x, y) Input Output (-3, 4) x y (3, -1) (4, -1) -3 4 (4, 3) 3 4 4 -1 -1 3 Graphing Domain: Set of all input values (x values) Range: Set of all output values (y values) {(-3, 14), (0, 7), (2, 0), (9, -18), (23, -99)} Function: Each input has exactly one output Domain Range -3 0 4 -2 1 7 Function Not a Function {(-7, 14), (9, -7), (14, 7), (7, 14)} Function Function Not a Function Function Rule: An equation that represents a function 𝒚 = 3𝒙 + 2 Output Dependent variable Input Independent variable 𝒇(𝒙) = 3𝒙 + 2 Read: f of x p. 65:10-24 Evaluate the function for x = 4 𝒇 𝒙𝟒 = 3(𝟒) 3𝒙 + 2 𝒇(𝟒) = 14 (4,14) 𝒈 𝒙 = −4𝒙 + 1 for 𝑥 = −3 𝒈 −𝟑 = −4(−𝟑) + 1 𝒈(−𝟑) = 13 (-3,13)