2 Linear Function a function of first degree polynomial that are of the form 1

# 2 linear function a function of first degree

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2. Linear Function – a function of first-degree polynomial that are of the form 𝑓𝑓 𝑥𝑥 = 𝑐𝑐 1 𝑥𝑥 + 𝑐𝑐 0 , 𝑐𝑐 1 0. 3. Quadratic Function – a function of the form 𝑓𝑓 𝑥𝑥 = 𝑎𝑎𝑥𝑥 2 + 𝑏𝑏𝑥𝑥 + 𝑐𝑐 , 𝑎𝑎 ≠ 0. 4. Rational Function – the quotient of two polynomial functions that are of the form 𝑓𝑓 𝑥𝑥 = 𝑔𝑔 ( 𝑥𝑥 ) ( 𝑥𝑥 ) , ( 𝑥𝑥 ) 0. 5. Absolute Value Function – a function of the form 𝑓𝑓 𝑥𝑥 = 𝑥𝑥 . OTHER TYPES OF FUNCTIONS 1. Power Function – a function of the form 𝑓𝑓 𝑥𝑥 = 𝑥𝑥 𝑛𝑛 where n is any real number. 2. Polynomial Function – any function of the form 𝑓𝑓 𝑥𝑥 = 𝑐𝑐 𝑛𝑛 𝑥𝑥 𝑛𝑛 + 𝑐𝑐 𝑛𝑛−1 𝑥𝑥 𝑛𝑛−1 + + 𝑐𝑐 1 𝑥𝑥 + 𝑐𝑐 0 . 3. Greatest Integer Function – a function of the form 𝑓𝑓 𝑥𝑥 = 𝑥𝑥 . The value 𝑥𝑥 is the greatest integer that is less than or equal to x. (e.g. 4.4 = 4 ) 4. Radical Function – a function of the form 𝑓𝑓 𝑥𝑥 = 𝑛𝑛 𝑥𝑥 , where x is an integer. TYPES OF FUNCTIONS Examples: Determine the type of function of the following. a. 𝑓𝑓 𝑥𝑥 = 𝑥𝑥−3 𝑥𝑥+7 Rational b. 𝑓𝑓 𝑥𝑥 = 3 𝑥𝑥 4 + 8 𝑥𝑥 3 4 𝑥𝑥 2 + 2 Polynomial c. 𝑓𝑓 𝑥𝑥 = 𝑥𝑥 4 Power d. 𝑓𝑓 𝑥𝑥 = 18 Constant e. 𝑓𝑓 𝑥𝑥 = 11 − 2𝑥𝑥 Linear f. 𝑓𝑓 𝑥𝑥 = 2𝑥𝑥 − 1 Absolute g. 𝑓𝑓 𝑥𝑥 = 𝑥𝑥 Greatest Integer DOMAIN AND RANGE OF GRAPHS OF FUNCTIONS Linear Function DOMAIN AND RANGE OF GRAPHS OF FUNCTIONS Quadratic Function DOMAIN AND RANGE OF GRAPHS OF FUNCTIONS Cube Function DOMAIN AND RANGE OF GRAPHS OF FUNCTIONS Square Root Function DOMAIN AND RANGE OF GRAPHS OF FUNCTIONS Cube Root Function DOMAIN AND RANGE OF GRAPHS OF FUNCTIONS Absolute Value Function DOMAIN AND RANGE OF GRAPHS OF FUNCTIONS Rational Function DOMAIN AND RANGE OF GRAPHS OF FUNCTIONS Greatest Integer Function DOMAIN: −∞ , RANGE: 𝒙𝒙 𝒙𝒙 𝒊𝒊𝒊𝒊 𝒂𝒂𝒂𝒂 𝒊𝒊𝒂𝒂𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊 GENERAL MATHEMATICS EVALUATION OF FUNCTIONS Learning Competencies At the end of the lesson, you are expected to: 1. State the steps of evaluating function; 2. Define function notation; 3. Evaluate function; and 4. State and apply the rules of addition, subtraction, multiplication and division of function. EVALUATION OF FUNCTIONS EVALUATION OF FUNCTIONS Given: 𝑓𝑓 𝑥𝑥 = 3𝑥𝑥 + 1, where x is a set of first 3 even numbers. How do you use functional notation in evaluating function? The function notation 𝑦𝑦 = 𝑓𝑓 𝑥𝑥 tells you that y is a function of x. 𝑦𝑦 = 𝑓𝑓 𝑥𝑥 𝑦𝑦 = 3𝑥𝑥 + 1 𝑓𝑓 ( 𝑥𝑥 ) = 3𝑥𝑥 + 1 The name of the function is f.  #### You've reached the end of your free preview.

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• Winter '19
• Michael Rubio
• Algebraic Expressions
• • • 