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- Brigham Young University
- Calculus
- Calculus 112
- Wadley
- Calc Test 1

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*ln*x=y is
*e*^{y}=x
*lne=*

even function

f(-x)=f(x)

how will I know if a function is even?

it will be symmetrical across the y-axis

how will I know if a function is odd?

it will be symmetrical across the origin

f(-x) = -f(x)

how do I make a horizontal compression of a graph?

y=2x

how do I make a horizontal stretch in a graph?

y=1/2x

what defines a one-to-one function?

-horizontal line test

-never has same y value twice

what is the domain of f^{-1}?

the range of f

what is the range of f^{-1}?

the domain of f

log_{a}x=y

equals

a^{y}=x

log_{a}(xy)=

log_{a}x+log_{a}y

log_{a}(x/y)=

log_{a}x-log_{a}y

log_{a}(x^{r})=

rlog_{a}x

log_{e}x=

lnx

1

change of base

log_{a}x=

frac{log_{b}x}{log_{b}a}

lim_{x->a}[f(x)+g(x)]=

lim_{x->a}f(x)+lim_{x->a}g(x)

lim_{x->a}[cf(x)]=

c lim_{x->a}f(x)

lim_{x->a}[f(x)g(x)]=

lim_{x->a}f(x)\times lim_{x->a}g(x)

lim_{x->a}\frac{f(x)}{g(x)}=

\frac{lim_{x->a}f(x)}{lim_{x->a}g(x)} lim_{x->a}g(x)\not 0

if 0<\left \lceil x-a\right \rceil<\delta then \left \lfloor f(x)-L\right \rfloor<\epsilon

lim_{x->-3}(7x-9)=-30

a= -3

L=-30

what does the law of absolute values say about this?

I5-2xI>3

5-2x>3 or

5-2x<-3

what does the graph of a parabola look like?

y=ax^{2}+bx+c

what is the equation for the vertex of a parabola?

v(-b/2a, (4ac-b^{2})/4a)

from ax^{2}+bx+c

how do I find the axis line for a parabola?

it is, x=-b/2a

what is the discriminant?

b^{2}-4ac

what if the discriminant is negative?

then the function has no real roots

what does i equal?

i=\sqrt{-1} so that i^{2}= -1

every polynomial with degree "n" has how many roots?

n number of roots!!!

Descartes Rule of Signs

- # of positive real roots > or = # of sign changes in P(x)
- # of negative roots > or = # of sign changes in P(-x)

Law of Sines

sinα/a = sinβ/b = sinγ/c

α + β + γ = 180°

Law of Cosines

a^{2 }= b^{2} + c^{2} - 2bc cosA

A being an angle and the rest sides

tangent graph

sine graph

cosine graph

the graph of x^3

s shaped

graph of ln(x)

How do you find the vertical asymptotes?

Set the denominator of the original equal to zero. VA occur where x is not defined.

About this deck

Author: Shawn G.

Created: 2014-04-28

Updated: 2014-04-28

Size: 38 flashcards

Views: 9

Created: 2014-04-28

Updated: 2014-04-28

Size: 38 flashcards

Views: 9

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