exam 1 formulas Flashcards
triangle
A= 1/2bh P= a+b+c
rectangle
A=lw
P=2(l+w)
trapezoid
A=1/2(a+b)h
P= a+b+c+d
ellipse
A=πab
square
A=a^2
P= 4a
parallelogram
A=bh
P= 2(a+b)
circle
A=πr^2
C=2πr
sector
A=1/2r^2θ
rectangular prism
SA= 2(wh+lw+lh) or x^2+4xh
V=lwh
*Rectangular Box
cylinder
SA= 2πr^2+2πrh
V= πr^2h
*Cylinder
guidelines for modeling w functions
- express model in words
- choose the variable
- set up the model
- use model
story problem steps
- get the question
- identify the variable(s)
- build equations
- solve
- ask “does my answer make sense?”
- state answer as a sentence
transformations steps
- sketch basic graph
- do horizontal shifts
- do reflections
- do vertical shifts
domain restrictions
1/x ;x≠0
√x ;x≥0 *n is even
1/√x ;x>0 *n is even *root is alone
inverse functions
- f(x1) ≠ f(x2)
- f(x1) = f(x2)
f^-1(y)=x; f(x)=y
cancellation props of inverse functions
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
technique to find inverse functions
- interchange x+y roles
- solve for y in terms of x
- set f^-1(x)=y
average rate of change
f(b)-f(a)/b-a
*diff quotient (x=a; x=a+h)
f(a+h)-f(a)/h
domains for combining functions
(f+g), (f-g), and (fg) are D=A∩B
(f/g) is D{x∈A∩B I g(x) ≠ 0}
x= b _slope; y=a _slope
und; 0
inequalities steps
- move all nonzero terms to one side
- factor
- find interval
- sign chart w test values
- solve
complete the square steps
- make sure a=1
- subtract c (x^2+bx= -c)
- find (b/2)^2
- add that value to both sides
- factor
- take square rt of both sides
- solve
