Evaluating Functions and Operations on Functions 4 January

Evaluating Functions and Operations on Functions 4 January 2011

Function Notation y = x 2 – 4 f(x) = x 2 – 4 Identifies the equation as a function p Pronounced Indicates which variable the function is in terms of (the variable used in the function) f of x

Evaluating Functions Algebraically p Solve for the value of a function at a point. p f(x) = 2 x – 10; find f(6) p f(6) = 2(6) – 10 f(6) = 12 – 10 f(6) = 2 The value of x is 6. Replace x with 6 and solve.

Evaluating Functions Algebraically, cont. p. You can also evaluate functions with an expression pf(x) = 2 x – 10; find f(x+1) = 2(x+1) – 10 f(x+1) = 2 x + 2 – 10 f(x+1) = 2 x – 8

Your Turn p Complete problems 1 – 6 on the Evaluating Functions handout

Solving for the Domain of Functions Algebraically p Domain Convention – unless otherwise stated, the domain (input or x-value) of a function is every number that produces a real output (y-value) No imaginary numbers or division by zero!

Solving for the Domain of Functions Algebraically, cont. p Always identify where the function equals a discontinuity or an imaginary number. Then solve for the values of x that don’t occur at those points. For square roots, set the radicand ≥ 0, then solve n For fractions, set the denominator ≠ 0, then solve n

Example #1 p Find the domain of f(x).

Example #2 p Find the domain of f(x).

Example #3 p Find the domain of f(x).

Your Turn: p Complete problems 7 – 14 on the Evaluating Functions handout

Evaluating Functions Graphically y = x 2 – 4 p Find f(2) means find the value of y when x = 2. f(x) = x 2 – 4

Your Turn: p Complete problems 15 – 18 on the Evaluating Functions handout