Functions 8/24/07

Functions – a rule that assigns each element of the domain (x) to exactly one element of the range (y)

Represented by a: -table
-graph

-equation

FUNCTIONS HAVE NAMES!!

f(x) is read “f of x” f(x)=x^3-3x+1

To solve, plug in the x value f(2)=2^3-3(2)+1 =3 ordered pair (2,3)

f(3y)=(3y)^3-3(3y)+1

f(☺)=☺^3-3(☺)+1

Domain of a Function – set of all x values that make “sense” for a situation

Restrictions are Imposed by: -context of the problem
-equation
-“us”

Equations with Restrictions: Fractions f(x) = 1/(x-5)
D: {x ≠ 5}
Square Roots f(x) = √x-4

D: {x ≥ 4}

Linear Functions

Never ending
Slope = rise/run = y2-y1/x2-x1 (any real #)
Straight
Slope-intercept form: y=mx+b (m=slope b=y-int)
Point-slope form: y-y1=m(x-x1)
Standard form: Ax=By=C
Perpendicular lines have negative reciprocal slopes
Parallel lines have equal slopes
Power of x is 1
Only one x-intercept and one y-intercept
Infinitely thin
Can be located in any quadrant of the x-y plane
Vertical lines have undefined slope
Horizontal line has 0 slope
Made up of an infinite amount of points

Handouts:

- EMRF Rubric
- Linear Equations – Problems

Homework:

- Prerequisite chapter activity due Tuesday
- P.65 #35, 38, 40, 41 due Tuesday
- P.75 #1-11 odd, 19-25 odd, 39, 43, 45, 47, 49 due Tuesday