September 12, 2012- Determine whether relationships between two variables are functions- Use function notation and evaluate functions- Find the domains of functions

Warm-up: Copy Quiz Topics• Linear Equations + word problems• Circle equation• x- and y-intercepts• Symmetry• Functions – evaluating

HW 1.4: Pg. 48-50 #9, 30, 31, 35, 57-69 odd

Quiz next class!

Check 1.2-1.3 Word Problems

Pg. 23 #72 Compare graphs

Pg. 36 #96 a) Largest increase 2002-03; least increase 2000-2001 b) slope from 94-2003 = 9.18 c)

#106 y(t) = -749.5t + 10,821.5; y(18) = -2669.5;

y(20) = -4168.5

#109 a) y(t) = 179.5t + 40,571; b) y(8) = 42,007;

y(10) = 42,366; c) m = 179.5

Lesson 1.4 Functions

A function f from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain (or set of inputs) of the function f, and the set B contains the range (or set of outputs).

• Verbally • Numerically • Graphically• Algebraically

“The input value x is the number of representatives from a state, and the output value of y is the number of senators.”

Four Ways to Represent a Function

(2, 11), (2, 10), (3, 8), (4, 5)

y = x2 + 2x + 1

Function Notation f(x)

Ex 1) Evaluating a function g(x) = -x2 + 4x + 1

Find the function value for the following:

a) g(2) b) g(t) c) g(x + 2)

g(2) = -(2)2 + 4(2) + 1

Replace all the x’s with the value of 2

g(2) = -4+ 8 + 1

g(2) = 5

g(t) = -(t)2 + 4(t) + 1

g(t) = -t2 + 4t + 1

g(x +2) = -(x+2)2 + 4(x + 2) + 1

g(x + 2) = -(x+2)(x+2) + 4(x + 2) + 1

g(x + 2) = -(x2 + 4x + 4)+ 4(x + 2) + 1

g(x + 2) = -x2 - 4x - 4+ 4x + 8 + 1

g(x +2) = -x2 + 5

Evaluating a piecewise-defined function (two or more equations over a specified domain)

Example 2) Evaluate the function when x = -1, 0, and 1

0,1

0,1)(

2

xx

xxxf

It gives you two conditions:

- Use x2 + 1, if x < 0

- Use x – 1, x ≥ 0

f(-1) = (-1)2 + 1

f(-1) = 1 + 1

f(-1) = 2

f(0) = 0 – 1

f(0) = – 1

f(1) = 1 – 1

f(1) = 0

Practice

1. Evaluate f(x) = x2 + 1 for:

a) f(-4) b) f(t2) c) f(t + 1)

2. Evaluate for:

a) f(-2) b) f(-1) c) f(0)

1,1

1,12)(

2 xx

xxxf

17 t4 + 1 t2 + 2t + 2

-3 -1 1

Finding the Domain of a Function

There are exceptions to what values can be inputted into a function.

For example:

A fraction A square root Quadratic

f (x) 1

x

f (x) x

{x| x is all real numbers, x ≠ 0} {x| x ≥ 0} {x| x is all real numbers}

Graphing the function also helps you see the domain.

f (x) x 2

PracticeFind the domain for each function

3. 4. 5.

5

1)(

x

xg 24)( xxf 13)( xxf

Evaluating a Difference QuotientThe difference quotient is the slope of the secant line that goes through two points of a function. This slope is very important in calculus where it is used

to define the derivative of function f.

h

xfhxf )()(

Answer 2x + h – 4

Evaluate f(x) = x2 – 4x + 7