Chapter 1 Flashcards

1
Q

X in a function

A

one and only one Y

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2
Q

Y in a function

A

as many x’s as it wants

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3
Q

In a fraction

A

The denominator cannot equal 0

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4
Q

In a radical

A

The radical is > or = to 0

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5
Q

Fun formula

A

f(x+h) - f(x)/h

h cannot equal 0

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6
Q

Increasing interval

A

where the graph is going up

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7
Q

Decreasing intervals

A

where the graph is going down

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8
Q

[]

A

including number

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9
Q

()

A

excluding number

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10
Q

Even

A

f(-x) = f(x)

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11
Q

Odd

A

f(-x) = -f(x)

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12
Q

Parent functions

A

search check

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13
Q

Vertical shifts

A

outside of function

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14
Q

Horizontal shifts

A

inside of function

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15
Q

Reflection across x-axis

A

outside of function

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16
Q

Reflection across y-axis

A

inside of function

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17
Q

Vertical stretch

18
Q

Vertical compression

19
Q

Horizontal stretch

20
Q

Horizontal compression

21
Q

Absolute value

A

makes any negative parts of a function positive (y values positive, not x)

22
Q

(f + g)(x) =

A

= f(x) + g(x)

23
Q

(f-g)(x) =

A

= f(x) - g(x), g(x) can’t be 0

24
Q

(fg)(x) =

A

= f(x) x g(x)

25
(f/g)(x) =
= f(x)/g(x)
26
(f º g)(x) =
= f(g(x))
27
(g º f)(x) =
= g(f(x))
28
To find a composites domain:
first consider the rules of the inside function, then the entire function
29
When dividing inequalities by a negative:
the sign flips
30
How to know if a function has an inverse:
1. one-to-one ratio 2. passes VLT and HLT 3. switch every (x, y) 4. symmetry around y=x axis 5. f(g(x)) = g(f(x)) = x
31
radicals:
plus or minus
32
When writing a function, if anything is in front of x:
Factor it: (3-x) + 2 -> (-(x + 3)) + 2
33
(xa)b
xab
34
xa ÷ x
xa - b
35
xa x xb
xa + b
36
(xy)a
xaya
37
(x/y)a
xa ÷ ya
38
x0
1
39
x-a
1/xa
40
xa/b
b√xa