PARIJATHA MATH FUNCTIONS FUNCTIONS WHAT IS A FUNCTION? ▸ A function can be thought of as a "machine" that provides exactly one output for each valid input. ⑴ ⑵ ⑶ ⑹ ⑿ ⒅ FUNCTIONS MAIN PARTS OF A FUNCTION ▸ Input ▸ Relationship ▸ Output ⑴ ⑵ ⑶ ⑹ ⑿ ⒅ FUNCTIONS EXAMPLES ▸ “Multiply by 6” ▸ 1×6=6 ▸ 2 × 6 = 12 ▸ 3 × 6 = 18 ⑴ ⑵ ⑶ ⑹ ⑿ ⒅ FUNCTIONS NOTATION ▸ f(x) = 6x ▸ f → function name ▸ x → input ▸ 6x → what to output ▸ Other notation f : x → 3x − 5 ▸ Sometimes functions have no names y = x 2 ⑴ ⑵ ⑹ ⑿ FUNCTIONS QUESTIONS ▸ For f(x) = 3x − 5 evaluate i) f(2) 2x + 6 For f : x → evaluate ▸ 3 f(3) f(2) = 3 × 2 − 5 i) =6−5=1 ii) f(1.5) ii) f(0) f(0) = 3 × 0 − 5 =−5 iii) f(−2) iii) f(−1) 2 For f(x) = x + 4 evaluate ▸ i) f(2) f(−2) = 3 × (−2) − 5 ii) f(6) = − 6 − 5 = − 11 iii) f(−1) FUNCTIONS INVERSE FUNCTION ▸ The inverse of a function is its reverse, i.e. it undoes the function’s effect ⑴ ⑵ ⑶ ⑹ ⑿ ⒅ FUNCTIONS NOTATION ▸ The inverse of a function f(x) is written as f −1 (x) ▸ Example: ▸ f(x) = 6x x −1 f (x) = ▸ 6 ⑴ ⑵ ⑹ ⑿ FUNCTIONS QUESTIONS Find the inverse of the following functions (i) f(x) = x + 2 f −1(x) = x − 2 ii) g(x) = 2x − 3 x+3 g (x) = 2 −1 x−3 For f(x) = evaluate 3 i) −1 f (2) ii) f −1 (3) FUNCTIONS QUESTIONS Find the inverse of the following functions (i) f(x) = x + 3 (i) f(x) = 4x ii) g(x) = x − 5 ii) f(x) = 2x + 5 iii) f(x) = x + 6 iii) f(x) = 3x − 6 iv) g(x) = x iv) x+4 f(x) = 2 v) h(x) = 2x vi) x p(x) = 3 v) 3x − 2 g(x) = 4 vi) 8x + 7 g(x) = 5 1 (i) f(x) = x + 3 2 1 ii) g(x) = x − 2 4 iii) f(x) = 4(3x − 6) iv) g(x) = 6(x + 3) v) h(x) = − 2(−3x + 2) 2 vi) p(x) = (4x − 5) 3