functions and relations

Question 1

domain

Answer 1

horizontal distance

Question 2

range

Answer 2

vertical distance

Question 3

if there is no stated domain or range?

Answer 3

assume it is R

Question 4

how to find domain and range of a coordinate set

Answer 4

list the x values for domain and the y values for range

Question 5

function

Answer 5

a relation where no coordinates has the same x value

Question 6

vertical lines test

Answer 6

determines if it is a function

must interest once

Question 7

what is a restriction?

Answer 7

a function but with a smaller domain

Question 8

one to one functions

Answer 8

every x value has a different y value

Question 9

horizontal line test

Answer 9

one intersection and it is one-to-one

two intersections and it is many to one

Question 10

how do you sketch a piecewise function?

Answer 10

sub in the value of the domain to find the y point and then sketch the graph normally keeping in the domain

Question 11

odd function

Answer 11

-f(x) = f(-x)

Question 12

even function

Answer 12

f(-x) + f(x)

Question 13

formula for the addition of ordinates

Answer 13

(f+g)(x) = f(x) + g(x)

Question 14

rule for composite functions

Answer 14

fog(x) = f(g(x))

Question 15

domain of composite functions

Answer 15

the domain of the inner function

Question 16

rules for inverse functions

Answer 16

must be one-to-one to have an inverse

Question 17

domain and range of inverse functions

Answer 17

domain of inverse is the range of the function and the range of the inverse is the domain of the function

Question 18

how to find the inverse?

Answer 18

swap x and y and solve for y

Question 19

power functions

Answer 19

x^r where r is a rational number

Question 20

strictly increasing and strictly decreasing

Answer 20

the turning point is included

Question 21

odd positive integer for power functions

Answer 21

goes through the first and third quadrants with a stationary point at 0,0
- gets steeper as the number increases

Question 22

even positive integer for power functions

Answer 22

quadratic shape

- gets steeper as the number gets bigger

Question 23

odd negative integer

Answer 23

hyperbola shape

Question 24

even negative integer

Answer 24

trunks shape

Question 25

even fractional power

Answer 25

half quadratic in first quadrant

Question 26

odd fractional power

Answer 26

half quadratic in first quadrant and double reflection of that in the third quadrant - an s

Question 27

how do you solve linear literal equations?

Answer 27

normally

Question 28

how do you solve simultaneous linear literal equations

Answer 28

normally

Question 29

what is the distance formula?

Answer 29

square root of (x2-x1) squared + (y2-y1) squared

Question 30

what is the midpoint formula?

Answer 30

x1+x2 divided by 2 and y1+y2 divided by 2

Question 31

gradient of a straight line

Answer 31

rise over run

Question 32

tangent of an angle of a slope

Answer 32

m= tan(angle) where the angle is the angle made with the positive x axis

Question 33

perpendicular line

Answer 33

m1 x m2 = -1

Question 34

parallel line

Answer 34

m1 = m2

Question 35

how do you calculate the shape of areas

Answer 35

divide into shapes you can calculate the areas of

Question 36

entries

Answer 36

numbers in a matrix

Question 37

dimension of a matrix

Answer 37

the number of rows and columns

Question 38

rows or columns listed first

Answer 38

rows and then columns

Question 39

when does A =B in matrices?

Answer 39

- same number of rows and columns | - same entries at the same points

Question 40

how do you add matrices?

Answer 40

add the corresponding numbers

Question 41

how do you subtract matrices?

Answer 41

subtract the corresponding numbers

Question 42

A + A (matrices)

Answer 42

= 2A

Question 43

how do you multiply matrices?

Answer 43

- multiply the first entry of row 1 of A by the first entry of column 1 of B - add that to the second entry of row 1 of A by the second entry of column 1 in B - only works if dimensions are the same

Question 44

does AB = BA?

Answer 44

no

Question 45

unique solution?

Answer 45

one intersection

Question 46

no solutions?

Answer 46

parallel

Question 47

infinite solutions

Answer 47

same line

Question 48

how to solve linear equations with more than two variables

Answer 48

eliminate a variable and then solve normally | - do this by multiplying or subtract etc.