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Unit 1 Functions: Definition, Notation,

and Evaluation

Compound inequalities

Has more

than 1 inequality sign

x≥ and x

Intersection

∩

Ex:3x+1>10 or 2x-7≤9

-1 -1 union +7 +7

x>3 ∪ x≤9

ex2:

3x+1

Function (domain)

x≠ -1/2 b/c 2x+1≠0 b/c denom ≠0

domain domain

f(x)=7x-1 p(x)=√3x+2

2x+1

evaluate: evaluate:

f(1) p(2/3)

7(1)-1 = 6 = 2 √3(2/3)+2= √2+2 = 2

2(1)+1 3

f(-1) p(0)

7(-1)-1= -8 = 8 √3(0)+2 =√2

2(-1)+1 -1

standard form linear equation

ax+by=c

A and B and C € ℤ

used when we combine 2 changing qualities that summed to something.

burgers $2.50 > total earnings &57

dogs $1.75 >

x= # burgers

y=# dogs > 2.5x+1.75=57

motion formula

h(t) = –gt2 + v0t + h0

where g=acceleration due to gravity- 9.8m/s2 - 32 ft/s2

v= starting velocity

(if an object is dropped v=0)

functions

f(x)=ax2+bx+c

f=h

x=t

a=-1/2g0

b=v0

c=h0

Difference

of square

(a+b)(a-b)=a2-b2

Ex:

(3x-4y) (3x+4y)=9x2-16y2

Let’s check: (3x-4y) (3x+4y)=9x2+12y-12y+16y2

«the middle

terms cancel out and you must distribute

If you have a binomial with a [term] even “n” –

[term] even “n” It is factorable as:

(√term

+ √term

)(√term

- √term

)

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