Chapter 1

Question 1

X in a function

Answer 1

one and only one Y

Question 2

Y in a function

Answer 2

as many x’s as it wants

Question 3

In a fraction

Answer 3

The denominator cannot equal 0

Question 4

In a radical

Answer 4

The radical is > or = to 0

Question 5

Fun formula

Answer 5

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

h cannot equal 0

Question 6

Increasing interval

Answer 6

where the graph is going up

Question 7

Decreasing intervals

Answer 7

where the graph is going down

Question 8

[]

Answer 8

including number

Question 9

()

Answer 9

excluding number

Question 10

Even

Answer 10

f(-x) = f(x)

Question 11

Odd

Answer 11

f(-x) = -f(x)

Question 12

Parent functions

Answer 12

search check

Question 13

Vertical shifts

Answer 13

outside of function

Question 14

Horizontal shifts

Answer 14

inside of function

Question 15

Reflection across x-axis

Answer 15

outside of function

Question 16

Reflection across y-axis

Answer 16

inside of function

Question 17

Vertical stretch

Answer 17

□f(x)

Question 18

Vertical compression

Answer 18

1/□f(x)

Question 19

Horizontal stretch

Answer 19

f(□x)

Question 20

Horizontal compression

Answer 20

f(1/□x)

Question 21

Absolute value

Answer 21

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

Question 22

(f + g)(x) =

Answer 22

= f(x) + g(x)

Question 23

(f-g)(x) =

Answer 23

= f(x) - g(x), g(x) can’t be 0

Question 24

(fg)(x) =

Answer 24

= f(x) x g(x)

Question 25

(f/g)(x) =

Answer 25

= f(x)/g(x)

Question 26

(f º g)(x) =

Answer 26

= f(g(x))

Question 27

(g º f)(x) =

Answer 27

= g(f(x))

Question 28

To find a composites domain:

Answer 28

first consider the rules of the inside function, then the entire function

Question 29

When dividing inequalities by a negative:

Answer 29

the sign flips

Question 30

How to know if a function has an inverse:

Answer 30

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

Question 31

radicals:

Answer 31

plus or minus

Question 32

When writing a function, if anything is in front of x:

Answer 32

Factor it:
(3-x) + 2 -> (-(x + 3)) + 2

Question 33

(x^a)^b

Answer 33

x^ab

Question 34

x^a ÷ x

Answer 34

x^{a - b}

Question 35

x^a x x^b

Answer 35

x^{a + b}

Question 36

(xy)^a

Answer 36

x^ay^a

Question 37

(x/y)^a

Answer 37

x^a ÷ y^a

Question 38

x⁰

Answer 38

1

Question 39

x^-a

Answer 39

1/x^a

Question 40

x^a/b

Answer 40

^b√x^a