Function-Notation in Calculus (Group1) 2B.pptx

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1. A function is a ‘job’ Function Notation

2. The notation f(x) defines a function named f. This is read as “y is a function of x.” The letter x represents the input value, or independent variable. The letter y is replaced by f(x) and represents the output value, or dependent variable. Function Notation

3. Function Notation f( x ) You are familiar with function notation like: y = 5 x + 3 or y= x 2 + 4 x + 6 y = f( x ) means that y is a function of x . You read f( x ) as ‘f of x ’. So, if y = x 2 + 2, we can also write f( x ) = x 2 + 2

4. Example If f( x ) = 3 x + 7, find: (a ) f(1) = 3(1) + 7 = 3 + 7 = 10 This means that our value of x is 1. So we substitute x with 1 (b) f(4) This means that our value of x is 4. So we substitute x with 4 = 3(4) + 7 = 12 + 7 = 19 (c) f(-2) = 3(-2) + 7 = -6 + 7 = 1 This means that our value of x is -2. So we substitute x with -2

5. Example Let f( x ) = 4 x 2 – 3, find: (a) f(3) = 4(3) 2 – 3 = 4(9) - 3 = 36 - 3 This means that our value of x is 3. So we substitute x with 3 (b) f(-5) This means that our value of x is -5. So we substitute x with -5 = 33 = 4(-5) 2 – 3 = 4(25) - 3 = 100 - 3 = 97

6. Try these… (1) Let f(x) = 7x – 8. Find the value of: (a) f(2) (b ) f(8) (c) f(-8) (2) Let f(x) = 3x 2 + 2. Find the value of each of these. (a) f(4) (b ) f(-1) (c) f(2 2 ) (3) Let g(x) = 3x 2 – 2x + 1. Find: (a) g(3) (b) g(-2) (c) g(0)

7. Example If g( x ) = 5 x - 9, then: (a) Solve g(x) = 21 This means that our expression is equal to 21 ⇒ 5 x – 9 = 21 ⇒ 5 x = 30 ⇒ x = 6 Now solve the equation! (b) Solve g(x) = -64 ⇒ 5 x - 9 = -64 ⇒ 5 x = -55 ⇒ x = -11 This means that our expression is equal to -64 Now solve the equation!

8. Example If f( x ) = x 2 – 3 x , then solve f(x) = 4 . This means that our expression is equal to 4 ⇒ x 2 – 3 x = 4 ⇒ x 2 – 3 x – 4 = 0 ⇒ (x - 4)(x + 1) = 0 Now solve the equation! ⇒ (x - 4) = 0 or (x + 1) = 0 ⇒ x = 4 or x = -1

9. Try these… (1) Let h(x) = 2x – 5. Solve h(x) = 7. (2) Let g(x) = 4x - 3. Solve g(x) = 0. (3) h(x) = x 2 – 2 (a ) Find h(3) and h(-6) (b ) Solve h(x) = 7 (4) Let f(x) = 3x 2 – 11x. (a) Find f(-3) (b) Solve f(x) = 20

10. Example If h( x ) = 2 x + 7 , then write an expression for: (a) h(3x) = 2(3x ) + 7 = 6x + 7 This means that our value of x is 3x. So we substitute x with 3x (c) 4h(x) = 4(2x + 7) This means we are multiplying h(x) by 4. = 8x + 28 (b) 3h(x) = 3(2x + 7) = 6x + 21 This means we are multiplying h(x) by 3.

11. Example Let f( x ) = x 2 + 7, then write an expression for: (a) f(x) +2 = ( x 2 + 7) + 2 = x 2 + 9 (b) f(x + 2) = ( x +2) 2 + 7 = ( x +2) ( x +2) + 7 This means we add 2 to f(x). This means that our value of x is (x + 2). So we substitute x with (x + 2) = x 2 + 4 x + 4 + 7 = x 2 + 4 x + 11

12. AGUDA, Mark Clifford ALCANTRA, John Alfred ALTURA, Marjorie CASTRO, Danny DELA CRUZ, Christian James DELA CRUZ, Jerimie CORSINO , Brian FABRO, Cristine GADONG, Karl Said GAGTAN, Darlfred John GOROSPE , Christian HADAP, Karren Jae Members: