Function Notation A function is a ‘job’

Function Notation f(x) You are familiar with function notation like: y = 5x + 3 or y= x2 + 4x + 6 y = f(x) means that y is a function of x. You read f(x) as ‘f of x’. So, if y = x2 + 2, we can also write f(x) = x2 + 2

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

Example Let f(x) = 4x2 – 3, find: (a) f(3) = 4(3)2 – 3 = 4(9) - 3 This means that our value of x is 3. So we substitute x with 3 (a) f(3) = 4(3)2 – 3 = 4(9) - 3 = 36 - 3 = 33 (b) f(-5) = 4(-5)2 – 3 This means that our value of x is -5. So we substitute x with -5 = 4(25) - 3 = 100 - 3 = 97

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) = 3x2 + 2. Find the value of each of these. (a) f(4) (b) f(-1) (c) f(22) (3) Let g(x) = 3x2 – 2x + 1. Find: (a) g(3) (b) g(-2) (c) g(0)

Example If g(x) = 5x - 9, then: (a) Solve g(x) = 21 ⇒ 5x – 9 = 21 This means that our expression is equal to 21 (a) Solve g(x) = 21 ⇒ 5x – 9 = 21 Now solve the equation! ⇒ 5x = 30 ⇒ x = 6 (b) Solve g(x) = -46 This means that our expression is equal to -46 ⇒ 5x – 9 = -46 ⇒ 5x = -55 Now solve the equation! ⇒ x = -11

This means that our expression is equal to 4 Example If f(x) = x2 – 3x, then solve f(x) = 4. ⇒ x2 – 3x = 4 This means that our expression is equal to 4 ⇒ x2 – 3x – 4 = 0 ⇒ (x - 4)(x + 1) = 0 Now solve the equation! ⇒ (x - 4) = 0 or (x + 1) = 0 ⇒ x = 4 or x = -1

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) = x2 – 2 (a) Find h(3) and h(-6) (b) Solve h(x) = 7 (4) Let f(x) = 3x2 – 11x. (a) Find f(-3) (b) Solve f(x) = 20

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

This means we add 2 to f(x). Example Let f(x) = x2 + 7, then write an expression for: (a) f(x) +2 = (x2 + 7) + 2 This means we add 2 to f(x). = x2 + 9 This means that our value of x is (x + 2). So we substitute x with (x + 2) (b) f(x + 2) = (x +2)2 + 7 = (x +2) (x +2) + 7 = x2 + 4x + 4 + 7 = x2 + 4x + 11

Try these… (1) Let g(x) = 5x + 6. Write an expression for: (a) g(3x) (b) 3g(x) (2) h(x) = x2 - 6. Write an expression for each of these. (a) 2h(x) (b) h2(x) (c) h(x) + 3 (d) h(x+3) (3) Let p(x) = 7 – 3x. Write an expression for: (a) 3p(x) (b) p(3x) (c) p(x) + 3 (d) p(x+3) (4) f(x) = 3x2 - 2x. 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.