Lesson 2: Operations on Functions PDF

LESSON 2 GENERAL MATHEMATICS Performs addition, subtraction, multiplication, and division, of functions.  EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3.  EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3....

LESSON 2 GENERAL MATHEMATICS Performs addition, subtraction, multiplication, and division, of functions.  EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3.  EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3. 𝑓 𝑥 = 2𝑥 + 1 𝑓 𝑥 = 2(3) + 1 𝑓 𝑥 =6+1 𝒇 𝒙 =𝟕  EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3. 2 𝑞 𝑥 = 𝑥 − 2𝑥 + 2 2 𝑞 𝑥 = (3) −2(3) + 2 𝑞 𝑥 =9−6+2 𝒒 𝒙 =𝟏  EVALUATION OF FUNCTIONS Evaluate the following functions at x = 3. 2 𝑓 𝑥 = 𝑥 + 3𝑥 + 9 2 𝑓 𝑥 = (3) +3(3) + 9 𝑓 𝑥 =9+9+9 𝒇 𝒙 = 𝟐𝟕  STEPS 1. Substitute the value of the 2 functions. 2. Combine like terms. EXAMPLES 1. f(x) = 2𝑥 − 5𝑥 + 4 ; 3 g(x) = 3𝑥 + 2𝑥 − 6 2 2. f(x) = 2𝑥 − 1 ; g(x) = 𝑥 + 𝑥 − 2 2 EXAMPLE: 1. 𝑓(𝑥) = 2𝑥 − 5𝑥 + 4 ; 3 2 𝑔(𝑥) = 3𝑥 + 2𝑥 − 6 𝒇+𝒈 𝒙 =𝒇 𝒙 +𝒈 𝒙 3 2 𝒇 + 𝒈 𝒙 = (2𝑥 −5𝑥 + 4) + (3𝑥 +2𝑥 − 6) 3 2 𝒇 + 𝒈 𝒙 = 2𝑥 +3𝑥 −5𝑥 + 2𝑥 + 4 − 6 𝟑 𝟐 𝒇 + 𝒈 𝒙 = 𝟐𝒙 +𝟑𝒙 −𝟑𝒙 − 𝟐 STEPS 1. Substitute the value of the 2 functions. 2. Combine like terms. EXAMPLE: 2. 𝑓(𝑥) = 2𝑥 − 1 ; 2 𝑔 𝑥 =𝑥 +𝑥 −2 𝒇+𝒈 𝒙 =𝒇 𝒙 +𝒈 𝒙 2 𝒇 + 𝒈 𝒙 = (2𝑥 − 1) + (𝑥 +𝑥 − 2) 2 𝒇 + 𝒈 𝒙 = 𝑥 + 2𝑥 + 𝑥 − 1 − 2 𝟐 𝒇 + 𝒈 𝒙 = 𝒙 + 𝟑𝒙 − 𝟑 STEPS 1. Substitute the value of the 2 functions. 2. Combine like terms.  STEPS 1. Substitute the value of the 2 functions. 2. Change the sign of the subtrahend 3. Combine like terms. EXAMPLES 1. 𝑓(𝑥) = 2𝑥 − 5𝑥 + 4 3 2. 𝑓(𝑥) = 2𝑥 − 1 ; 2 2 𝑔(𝑥) = 3𝑥 + 2𝑥 − 6 𝑔(𝑥) = 𝑥 + 𝑥 − 2  EXAMPLES STEPS 1. Substitute the value of the 2 functions. 1. 𝑓(𝑥) = 2𝑥 − 5𝑥 + 4 ; 3 2. Change the sign of the subtrahend. 2 3. Combine like terms. 𝑔(𝑥) = 3𝑥 + 2𝑥 − 6 𝒇−𝒈 𝒙 =𝒇 𝒙 −𝒈 𝒙 𝒇−𝒈 𝒙 3 2 = 2𝑥 − 5𝑥 + 4 − (3𝑥 +2𝑥 − 6) 3 2 𝒇−𝒈 𝒙 = 2𝑥 − 5𝑥 + 4 + (−3𝑥 −2𝑥 + 6) 3 2 𝒇−𝒈 𝒙 = 2𝑥 −3𝑥 −5𝑥 − 2𝑥 + 4 + 6 𝟑 𝟐 𝒇 − 𝒈 𝒙 = 𝟐𝒙 −𝟑𝒙 −𝟕𝒙 + 𝟏𝟎  EXAMPLES STEPS 1. Substitute the value of the 2 functions. 2.𝑓(𝑥) = 2𝑥 − 1; 2. Change the sign of the subtrahend. 2 3. Combine like terms. 𝑔(𝑥) = 𝑥 + 𝑥 − 2 𝒇−𝒈 𝒙 =𝒇 𝒙 −𝒈 𝒙 𝒇−𝒈 𝒙 2 = 2𝑥 − 1 − (𝑥 +𝑥 − 2) 2 𝒇−𝒈 𝒙 = 2𝑥 − 1 + (−𝑥 −𝑥 + 2) 2 𝒇−𝒈 𝒙 = −𝑥 + 2𝑥 − 𝑥 − 1 + 2 𝟐 𝒇 − 𝒈 𝒙 = −𝒙 + 𝒙 + 𝟐  LAWS OF EXPONENT 𝑚 𝑛 𝑚+𝑛 1. Product rule; 𝑥. 𝑥 = 𝑥 𝑚 𝑛 𝑚.𝑛 2. Power rule; (𝑥 ) =𝑥 𝑛 𝑛 𝑛 3. Power of product; (𝑥𝑦) = 𝑥 𝑦 EXAMPLES 1. Multiplying a binomial to a monomial. f(x) = 5𝑥 g(x) = 𝑥 + 4 2. Multiplying a binomial to a binomial (FOIL METHOD) f(x) = 𝑥 + 3 g(x) = 𝑥 + 5 3. Multiplying a binomial to a trinomial f(x) = 9𝑥 − 5 g(x) = 6𝑥 + 𝑥 − 7 2  RULES OF DIVISION OF EXPONENT 𝑥𝑚 ; 𝑥 5 2 1. 𝑛 = 𝑥 𝑚−𝑛 = 𝑥 5−3 = 𝑥 𝑥 𝑥3 2. 𝑛 = 𝑤ℎ𝑒𝑛 𝑚 < 𝑛; 6 = 2 𝑥 𝑚 𝑥 4 1 𝑥 𝑥 𝑥 0 3. 𝑥 = 1 EXAMPLES 1. f(x) = 15 𝑥 15 2. f(x) = −4 𝑥 5 3. f(x) = 9 𝑥6 g(x) = 3 𝑥 9 g(x) = 2𝑥 8 g(x) = 9 𝑥 6