exam 1 formulas

Question 1

triangle

Answer 1

A= 1/2bh 
P= a+b+c

Question 2

rectangle

Answer 2

A=lw

P=2(l+w)

Question 3

trapezoid

Answer 3

A=1/2(a+b)h

P= a+b+c+d

Question 4

ellipse

Answer 4

A=πab

Question 5

square

Answer 5

A=a^2

P= 4a

Question 6

parallelogram

Answer 6

A=bh

P= 2(a+b)

Question 7

circle

Answer 7

A=πr^2

C=2πr

Question 8

sector

Answer 8

A=1/2r^2θ

Question 9

rectangular prism

Answer 9

SA= 2(wh+lw+lh) or x^2+4xh
V=lwh
*Rectangular Box

Question 10

cylinder

Answer 10

SA= 2πr^2+2πrh
V= πr^2h
*Cylinder

Question 11

guidelines for modeling w functions

Answer 11

1. express model in words
2. choose the variable
3. set up the model
4. use model

Question 12

story problem steps

Answer 12

1. get the question
2. identify the variable(s)
3. build equations
4. solve
5. ask “does my answer make sense?”
6. state answer as a sentence

Question 13

transformations steps

Answer 13

1. sketch basic graph
2. do horizontal shifts
3. do reflections
4. do vertical shifts

Question 14

domain restrictions

Answer 14

1/x ;x≠0
√x ;x≥0 *n is even
1/√x ;x>0 *n is even *root is alone

Question 15

inverse functions

Answer 15

1. f(x1) ≠ f(x2)
2. f(x1) = f(x2)

f^-1(y)=x; f(x)=y

Question 16

cancellation props of inverse functions

Answer 16

if f and f^-1 are inverse functions,
f^-1(f(x))=x
f^-1(f(y))=y
if f and f^-1 have the property *, we say f and f^-1 are inverse functions

Question 17

technique to find inverse functions

Answer 17

1. interchange x+y roles
2. solve for y in terms of x
3. set f^-1(x)=y

Question 18

average rate of change

Answer 18

f(b)-f(a)/b-a

*diff quotient (x=a; x=a+h)
f(a+h)-f(a)/h

Question 19

domains for combining functions

Answer 19

(f+g), (f-g), and (fg) are D=A∩B

(f/g) is D{x∈A∩B I g(x) ≠ 0}

Question 20

x= b _slope; y=a _slope

Answer 20

und; 0

Question 21

inequalities steps

Answer 21

1. move all nonzero terms to one side
2. factor
3. find interval
4. sign chart w test values
5. solve

Question 22

complete the square steps

Answer 22

1. make sure a=1
2. subtract c (x^2+bx= -c)
3. find (b/2)^2
4. add that value to both sides
5. factor
6. take square rt of both sides
7. solve