Introduction to Functions 31 January 2011

Functions – What do we remember about them? Think-Pair-Share Think about functions for 30 s. independently and silently Talk about functions for 1 m in your groups Share as a class

Review: Definition Function – a set (of points, an equation, or a graph) where each input has exactly one output

Review: Function Notation Domain (Input) Range (Output) Equation x y y = x2 – 4 f(x) f(x) = x2 – 4 In function notation, f(x) replaces y.

Review: Function Notation f(x) = x2 – 4 Pronounced f of x = x2 – 4 The variable inside the parentheses indicates which variable the function is in terms of (the variable used in the function) f( ) identifies the equation as a function You may also see other letters, ex. g( ) or h( )

Evaluating Functions f(#) f(x) = # Find the value of f(x) when x equals #. Solve for f(x)! f(x) = # Find the value of x when f(x) equals #. Solve for x!

Find f(#) f(x) = 2x – 10; f(6) f(x) = 2x – 10 f(6) = 2(6) – 10 The value of x is 6. Replace x with 6 in the function and solve for f(6).

Find f(#) – Showing Work f(x) = 2x – 10; f(6) f(x) = 2x – 10 f(6) = 2(6) – 10 f(6) = 12 – 10 f(6) = 2

Example g(x) = –x2 + 4x + 1 g(2) g(½)

Your Turn: Complete the 1st 2 columns of problems 1 – 4 on the “Evaluating Functions” handout

Answers: f(1) = –1; f(–3) = –9 h(2) = 0; h(1.5) = –0.75 g(0) = ; g(3) = undefined f(2) = 1; f(–2) = –1

Find f(#) When the # Is an Expression You can also evaluate functions with expressions f(x) = 2x – 10; f(x+1) f(x) = 2x – 10 f(x+1) = 2(x+1) – 10 f(x+1) = 2x + 2 – 10 f(x+1) = 2x – 8

Find f(#) When the # Is an Expression – Showing Work f(x) = 2x – 10; f(x+1) f(x) = 2x – 10 f(x+1) = 2(x+1) – 10 f(x+1) = 2x + 2 – 10 f(x+1) = 2x – 8

Example g(x) = –x2 + 4x + 1 g(x3) g(x + 2)

Your Turn: Complete the 3rd (and last) column of problems 1 – 4 on the “Evaluating Functions and Domain” handout

Find f(x) = # Remember, we’re solving for values of x that equal that indicated number. f(x) = 2x – 10; find f(x) = 0 f(x) = 2x – 10 0 = 2x – 10 10 = 2x 5 = x

Find f(x) = # – Showing Work f(x) = 2x – 10; find f(x) = 0 f(x) = 2x – 10 0 = 2x – 10 10 = 2x 5 = x

Example 1 f(x) = 2x2 – 3x + 1 Find f(x) = 3

Example 2 Find g(x) = 8

Your Turn: Complete problems 5 – 8 on the “Evaluating Functions” handout