![The function 𝑔 is define on the real numbers by
g 𝑥 = (𝑥2
+ 1)(3𝑥 − 5). What is the value of g 4 ?
Solution:
g 𝑥 = (𝑥2 + 1)(3𝑥 − 5), g 4 =?
g 4 = 42 + 1 [3(4) − 5], substitute x with 4
g 4 = (16 + 1)(12 − 5), simplify 42 , multiply 3(4)
g 4 = (17)(7), add (16 + 1), subtract (12 - 5)
g 4 = 119
The value of 𝑔 4 is 119.](https://image.slidesharecdn.com/evaluatingfunctions-210704123410/85/Evaluating-functions-14-320.jpg)
Evaluating functions
- 2. EVALUATING FUNCTIONS General Math Week 1, LC Code: (M11GM - Ia – 1)
- 3. Learning Competency The learner evaluates a function. (M11GM - Ia – 1)
- 4. Learning Objectives At the end of this video, you are able to: 1. Recall the difference between function and relation; 2. Recall on the four ways to represent a function; and 3. Evaluate a function.
- 5. What is the difference between function and relation? Function • A function is a relation that is for each input there is only one output. • A function is a set of ordered pairs (x,y) such that no two ordered pairs have the same x-element (abscissa). • A function can be a one-to-one or many-to-one correspondence but can not be a one-to-many correspondence. Relation • A relation is a set of inputs and outputs. • A relation is a set of ordered pairs (x,y). • A relation can be one-to-one, one-to- many and/or many-to-one correspondence.
- 6. Fact or Bluff 1. All functions are relations. Answer: Fact 2. All relations are functions. Answer: Bluff 3. A function is a set of ordered pairs (x,y) such that no two ordered pairs have the same y-element. Answer: Bluff 4. A student with a unique identification number is an example of a function. Answer: Fact 5. Not all functions are relations. Answer: Bluff
- 7. Four Ways to represent a FUNCTION Sets of Ordered Pairs Table of Values Graphs Equation
- 8. Which of the following sets of ordered pairs are functions? Answer: The sets in a and b are functions. Multiple Choice a. h = {(0,0),(1,1),(2,2),(3,3),(4,4),...} d. H = {(0,0),(0,1),(2,2),(3,3),(4,4),...} b. g = {(0,0),(1,0),(2,0),(3,0),(4,0),...} c. f = {(-2,0),(-2,1),(-2,2),(-2,3),(-2,4),...}
- 9. Which of the following tables below represent a function? x 0 1 2 3 y 0 1 2 3 x 1 1 1 1 y -4 -2 0 2 x -1 0 1 2 y 2 2 2 2 x 2 4 2 4 y -2 0 2 6 Answer: A and C A B C D
- 10. Which of the following graphs can be graphs of functions? Answer: a, b and c
- 11. Which of the following equations represent a function? Answer: a, c and d 𝒃. 𝒙𝟐 + 𝒚𝟐 = 𝟏 d. 𝒚 = 𝟏𝟎𝟎𝒙 𝒂. 𝒚 = 𝟐𝒙𝟐 − 𝟐𝒙 + 𝟐 c. 𝒚 = 𝟐𝒙 + 𝟏
- 12. Evaluating a function means replacing the variable x in the function with a given number or expression. For example, evaluate the function 𝑓 𝑥 = 2𝑥 + 4 𝑓𝑜𝑟 𝑥 = 5. Just replace the variable “x” with “5”: 𝑓 5 = 2 5 + 4 = 14 Answer: f(5)=14 Evaluating Functions
- 13. The function f is define on the real numbers by 𝑓 𝑥 = 2 + 𝑥 − 𝑥2 . What is the value of 𝑓 −3 ? Solution: 𝑓 𝑥 = 2 + 𝑥 − 𝑥2, 𝑓 −3 =? 𝑓 −3 = 2 + (−3) − (−3)2 substitute x with -3 𝑓 −3 = 2 + −3 − 9 simplify (−32) 𝑓 −3 = −10 The value of 𝑓 −3 is − 10.
- 14. The function 𝑔 is define on the real numbers by g 𝑥 = (𝑥2 + 1)(3𝑥 − 5). What is the value of g 4 ? Solution: g 𝑥 = (𝑥2 + 1)(3𝑥 − 5), g 4 =? g 4 = 42 + 1 [3(4) − 5], substitute x with 4 g 4 = (16 + 1)(12 − 5), simplify 42 , multiply 3(4) g 4 = (17)(7), add (16 + 1), subtract (12 - 5) g 4 = 119 The value of 𝑔 4 is 119.
- 15. Quiz Evaluate the following functions at 𝑥 = 2. 1. 𝑓 𝑥 = 2𝑥 + 1 2. 𝑞 𝑥 = 𝑥2 − 2𝑥 + 2 3. 𝑔 𝑥 = 𝑥 + 7 4. 𝑟 𝑥 = 6𝑥−2 𝑥+3 5. 𝑟 𝑥 = 4𝑥 − 1 Answer: 1. 𝑓 2 = 2𝑥 + 1= 2(2)+1 = 4 + 1 = 5 2. 𝑞 2 = 𝑥2 − 2𝑥 + 2 = 22 − 2 2 + 2 = 4 − 4 + 2 = 2 3. 𝑔 2 = 𝑥 + 7 = 2 + 7 = 9 = ±3 4. 𝑟 2 = 6𝑥−2 𝑥+3 = 6 2 −2 2+3 = 12−2 5 = 10 5 = 2 5. 𝑟 𝑥 = 4𝑥 − 1 = 42 − 1 = 16 − 1 = 15