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Section 4-7 Day 2 Graphing Functions Objective: Students will use function notation to graph and compare parent graphs. Standard: A.CED.2 , F.IF.7 , F.BF.3, F.IF.2 Example 1 Find the value of x so that the function has the given value. f(x) = 3x – 2 ; 10 This means f(x) = 10. Solve for x. f(x) = 3x – 2 10 = 3x – 2 +2 +2 12 = 3x 3 3 4=x Parent Functions and Families of Functions • A family of functions is a group of functions with similar characteristics. • For example: functions of the form f(x) = mx + b constitute the family of linear functions. • The most basic linear function in the family is called the parent linear function, which is: f(x) = x Y-intercept = b = 0 Slope = m = 1 (-1,-1) (-2,-2) (2,2) (1,1) (0,0) Example 2 • Changing the y-intercept will SHIFT your parent function up or down. Graph f(x) = x and the following on the same graph. Compare the graph with the graph of f(x) = x f(x) = x a. f(x) = x + 4 Shifts UP 4 b. f(x) = x – 3 Shifts DOWN 3 In General: If b > 0, Shift UP If b < 0, Shift DOWN Example 3 • Changing the SLOPE will change the STEEPNESS of your parent function. Also called stretch or shrink. Graph f(x) = x and the following on the same graph. Compare the graph with the graph of f(x) = x f(x) = x a. f(x) = 3x Steeper or Stretch b. f(x) = ½ x Less steep or Shrink c. f(x) = -2x Reflects and Steeper/Stretch In General for Slope: • If |m| > 0, then the graph is STEEPER or a STRETCH. • If 0< |m| < 1 (basically a fraction less than one), then the graph is LESS STEEP or a SHRINK. • If m is NEGATIVE , then the graph REFLECTS. Homework Section 4-7 Pg. 266-267 14 - 17, 23 - 34, 39, 41, 42