Functions

Kudos Know – How to identify functions. Know how to map relations. Know vocab… RelationMapping Diagram DomainFunction Notation Range Vertical Line Test Control VariableDependent Variable Understand what makes a relation a function. Do- Be able to identify functions, graph relations, and evaluate using function notation. 2.1 Relations and Functions

Control Variable …is a variable that determines or controls another variable.

Domain The domain of a function is all possible values of the control variable.

Dependent Variable …is a variable that is determined by or depends on another variable.

Range The range of a function is all possible values of the dependent variable.

To help you remember…. Control variable Dependent variable

“_____ depends on ____” Fastest walking speed : leg length Definition : word Radius: area of a circle Person: birthday Reciprocal : every real number (except 0) Hours worked : salary earned.

“_____ depends on ____” This variable goes on the y-axis This variable goes on the x-axis

Which axis?? Hours workedSalary

Which axis?? Area of a circleRadius

Which axis?? Leg length Walking speed

Which axis?? Every real number (except 0) Reciprocal

Relation Ex1) Graph the coordinate points: A relation is a set of pairs of input (x) and output (y) values. Written: {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}. (–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)

Relation Domain – the set of all inputs of a function (x-coordinates) Domain: {-3, -2, 0, 1, 2 } Range - the set of all outputs of a function (y-coordinates) Range: { -2, 2, 3, 4 } {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}

Relation Ex2) Write the ordered pairs for the relation. Find the domain and range.

Mapping Diagrams DomainRange Ex3) {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}.

Functions A function is a relation in which each input value is paired with only one output value. DomainRangeDomainRange Function?

Is it a function? Yes! Remember the vertical line test?

Is it a function? No! Remember the vertical line test?

Is it a function? No!

Is it a function? Yes! Stop?

Notation for functions y = f(x) say “f of x ” (not f times x) Control variable is the x Dependent variable is the y f(3) = 8 means the value of f at 3 is 8

Use f(x) = x 2 Find f(4) Find f(-5) Find f(a)

Expand (x+3) 2 x 2 + 3x +3x +3 2 x 2 + 6x + 9

Expand (x+y) 2 x 2 + xy +xy + y 2 x 2 + 2xy + y 2

Use f(x) = x 2 + 2x Find f(3) Find f(-2) Find f(c + d)

Planner Time! HW: 7, 12, 13, 17, 20, 21, 23, 25, 33, 37, 39, 41, 46, 47

Planner (and Test) Time! #13 p , 6-8, 10,11,13,16-24, When a question asks you to explain, you must use complete sentences in your answer.