SE A STORY OF FUNCTIONS Lesson 10 M3 ALGEBRA I Lesson Summary ALGEBRAIC FUNCTION: Given an algebraic expression in one variable, an algebraic function is a function f:D - Y such that for each real number x in the domain D. f(x) is the value found by substituting the number x into all instances of the variable symbol in the algebraic expression and evaluating. The following notation will be used to define functions going forward. If a domain is not specified, it is assumed to be the set of all real numbers. For the squaring function, we say Let f(x) = x². For the exponential function with base 2, we say Let f (x) = 2*. When the domain is limited by the expression or the situation to be a subset of the real numbers, it must be specified when the function is defined. For the square root function, we say Let f(x) = Vx for x 2 0. To define the first 5 triangular numbers, we say Let f (x) = xx+ for 1 < x< 5 where x is an integer. Depending on the context, one either views the statement "f(x) = Vx" as part of defining the function f or as an equation that is true for all x in the domain of f or as a formula. Problem Set 1. Let f(x) = 6x – 3, and let g(x) = 0.5(4)*. Find the value of each function for the given input. 0.54)=0.5 0:5(4)- 0,125 0:5(4)2 m. g(-3) 0.5(4) 0.0078 0.54)=128 9(V2) 0:54)= 3.55 6.5)ニ」 60) - 3 0-3 f(0) j. g(0) a. b. f(-10) k. g(-1) 6610)-3 -60- 66-3 12-3 C. f(2) I. g(2) d. f(0.01) f(11.25) n. g(4) e. f. f(-v2) 60.6)-3 0.06-3 O. g. fG) C(1,25)-3 67.5-3 p. g h. f(1) + f(2) q. g(2) + g(1) f(6) – f(2) bEVa)-3 -8,48-3 i. g(6) – g(2) r. 10-3 EUREKA MATH Lesson 10: Representing, Naming, and Evaluating Functions This work is derived from Eureka Math"and licensed by Great Minds. ©2015 Great Minds. eureka-math.org ALGI-M3-SE-B1-LL0-05.2015