Function Notation A function is a job Function
Function Notation A function is a ‘job’
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
Example If f(x) = 3 x + 7, find: (a) f(1) = 3(1) + 7 =3+7 = 10 (b) f(4) = 3(4) + 7 = 12 + 7 = 19 (c) f(-2) = 3(-2) + 7 = -6 + 7 =1 r u o t a h st n a e m e w o This S. is 1 x f o e h 1 t i valu w x ute t i t s b u s ur o t a h t ns a e m s we o Thi S. 4 is x f o e 4 h t i valu w ex t u t i t s sub ur o t a h t ans e e m s w i o Th S. s -2 i x f o h -2 t i value w x te u t i t s b su
Example Let f(x) = 4 x 2 – 3, find: (a) f(3) = 4(3)2 – 3 = 4(9) - 3 = 36 - 3 = 33 (b) f(-5) = 4(-5)2 – 3 = 4(25) - 3 = 100 - 3 = 97 r u o t a h st n a e m e w o This S. is 3 x f o e h 3 t i valu w x ute t i t s b u s r u o t a h st n a e e m w o This S. s -5 i x f o h -5 t i value w x te u t i t s b su
Try these… (1) Let f(x) = 7 x – 8. Find the value of: (a) f(2) (b) f(8) (c) f(-8) (2) Let f(x) = 3 x 2 + 2. Find the value of each of these. (a) f(4) (b) f(-1) (c) f(22) (3) Let g(x) = 3 x 2 – 2 x + 1. Find: (a) g(3) (b) g(-2) (c) g(0)
Example If g(x) = 5 x - 9, then: (a) Solve g(x) = 21 ⇒ 5 x – 9 = 21 ⇒ 5 x = 30 ⇒x=6 (b) Solve g(x) = -46 ⇒ 5 x – 9 = -46 ⇒ 5 x = -55 ⇒ x = -11 r u o t a h st n a e 1 2 m o t l This a qu e s i n sio expres n! o i t a u eq e h t e lv Now so ur o t a h t ans e m -46 s o i t l Th a u eq s i n o i s expres n! o i t a u eq e h t e v l Now so
Example If f(x) = x 2 – 3 x, then solve f(x) = 4. x 2 – ⇒ 3 x = 4 ⇒ x 2 – 3 x – 4 = 0 ⇒ (x - 4)(x + 1) = 0 ⇒ (x - 4) = 0 or (x + 1) = 0 ⇒ x = 4 or x = -1 r u o t a h st n a e m o 4 t l a This u q e s i n o i s expres n! o i t a u eq e h t e lv o s w o N
Try these… (1) Let h(x) = 2 x – 5. Solve h(x) = 7. (2) Let g(x) = 4 x - 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) = 3 x 2 – 11 x. (a) Find f(-3) (b) Solve f(x) = 20
Example If h(x) = 2 x + 7, then write an expression for: (a) h(3 x) = 2(3 x) + 7 = 6 x + 7 (b) 3 h(x) = 3(2 x + 7) = 6 x + 21 (c) 4 h(x) = 4(2 x + 7) = 8 x + 28 ur o t a h t ans e e m s w i o Th S. s 3 x i x f o 3 x h t i value w ex t u t i t s sub e r a e w ans e m 3. s i y b Th ) x ( gh n i y l p i t mul e r a e w ans e m. 4 s i y b Th ) h(x g n i y l multip
Example Let f(x) = x 2 + 7, then write an expression for: (a) f(x) +2 = 7) + 2 = x 2 + 9 (x 2 + (b) f(x + 2) = (x +2)2 + 7 = (x +2) + 7 = x 2 + 4 x + 4 + 7 = x 2 + 4 x + 11 o t 2 d d a we s n a e This m f(x). ue l a v r u to a h t s n e ea This m (x + 2). So w ) of x is x with (x + 2 ute t i t s b u s
Try these… (1) Let g(x) = 5 x + 6. Write an expression for: (a) g(3 x) (b) 3 g(x) (2) h(x) = x 2 - 6. Write an expression for each of these. (a) 2 h(x) (b) h 2(x) (c) h(x) + 3 (d) h(x+3) (3) Let p(x) = 7 – 3 x. Write an expression for: (a) 3 p(x) (b) p(3 x) (c) p(x) + 3 (d) p(x+3) (4) f(x) = 3 x 2 - 2 x. Write an expression for each of these. (a) f(x – 1) (b) f(x) - 1 (c) f(-x) (d) -f(x)
Self Assessment Do you understand how to use and solve problems involving function notation? Yes – I fully understand the topic. Mostly – I just need a little more practice. Not really – I am finding this topic quite difficult.
- Slides: 12