Studied by 51 people

5.0(1)

get a hint

hint

1

Solving Linear eqns & inequalities

isolate the variable

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2

Solving Quadratic eqns & inequalities

isolate zero

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3

Solving polynomial eqns & inequalities

isolate zero

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4

Solving Rational eqns & inequalities

multiply by the LCD

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5

Solving absolute value eqns & inequalities

isolate absolute value

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6

solving absolute value eqns

|a| =

a, if a>0

-a, if a<0

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7

solving absolute value ineqalities

|f(x)| > c means…

f(x)>c

or

f(x)< -c

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8

solving exponential equations

isolate the power

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9

solving radical eqns

isolate the radical

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10

solving log eqns

write as the log of one expression and then isolate the log

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11

solve trig eqns

1) isolate the trig ratio

2) use zero product property

3) use a trig identity

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12

to translate a graph up

add a #

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13

to translate a graph down

subtract a #

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14

to translate a graph right

subract a # “within”

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15

to translate a graph left

add a # “within”

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16

to vertically stretch a graph

multiply by a # c (c>1)

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17

to vertically shrink a graph

multiply by a # c (0<c<1)

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18

f(x) + k

translates a graph up k units

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19

f(x) - k

translates a graph down k units

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20

kf(x), where k>1

vertical stretch

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21

kf(x), where 0<k<1

vertical shrink

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22

f(x+h)

translates graph left h units

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23

f(x-h)

translates graph right h units

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24

to find x-intercepts

substitute 0 for y

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25

to find y-intercept

substitute 0 for x

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26

how to find inverse function

1) replace f(x) with y

2) switch x & y

3) solve for the new y

4) replace g(x) for the new y

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27

properties of inverse function

1) symmetric with y=x

2) f(g(x)) = g(f(x)) = x

3) one-to-one function

4) Domain & Range are interchanged

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28

f(kx), where k>1

horizontal shrink

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29

f(kx), where 0<k<1

horizontal stretch

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30

f(-x)

reflection across y-axis

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31

-f(x)

reflection across x-axis

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32

-f(-x)

reflection through origin

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33

f(|x|)

reflection of QI & QIV through y-axis (lose QII & QIII)

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34

|f(x)|

Reflection of QIII and QIV through x-axis (lose QI & QII)

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35

1/f(|x|)

y → 0^{+} <-> y → +∞

y → 0^{-} <-> y → -∞

y = 0 <-> y is undefined

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36

f(h-x)

= f(x+h) then replace xby - x (reflection of f(x+h) through y-axis)

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|f(x)| defined as a piecewise function

f(x) for all x where f(x) ≥ 0

-f(x) for all x where f(x) < 0

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38

even function

a function that is symmetric to itself through the y-axis; f(-x) = f(x)

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39

odd function

a function that is symmetric to itself through the origin; -f(x) = f(x)

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40

f(x) = x

linear family

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41

f(x) = x^{2}, x^{4}, x^{6}

parabolic family

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42

f(x) = x^{3}, x^{5}, x^{7}

cubic family

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43

f(x) = x^{1/2}, x^{1/4}, x^{1/6}

square root family

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44

f(x) = x^{1/3}, x^{1/5}, x^{1/7}

cubic root family

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45

f(x) = x^{-2}, x^{-4}, x^{-6}

bell curve family

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46

f(x) = x^{2/3}, x^{4/5}, x^{6/7}

Bird Family

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47

f(x) = [|x|]

greatest integer function

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48

f(x) = |x|

absolute value

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49

f(x) = ax² + bx + c

parabola family

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50

Vertex of f(x) = ax² + bx + c?

Vertex → (h,k)

h = -b/2

k = f(-b/2a)

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51

f(x) = a_{n}x^{n} + a_{n-1}x^{n-1} + .. a_{0; n is odd}

1) outside behavior → cubic

2) intercepts

3) relative extrema (n-1)

4) symmetry

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52

f(x) = (a_{n}x^{n} + a_{n-1}x^{n-1} + .. a_{0) /} (b_{m}x^{m} + b_{m-1}x^{m-1} + .. b_{0)}

1) asymptotes

2) intercepts

3) symmetry

4) plot points if needed

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53

to find vertical asymptotes

set denominator of simplified rational expression to 0

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54

to find horizontal asymptotes of rational functions

n=m, H.A. @ y=a/b

n<m, H.A. @ y = 0

n>m, no H.A.

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55

f(x) = (c-x²)^{1/2 }, _{c>0}

circular function

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56

f(x) = (x²-c)^{1/2 }, _{c>0}

hyperbolic function

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57

f(x) = (x²+c)^{1/2 }

hyperbolic function

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