algebra / functions

Question 1

how to transform graph

Answer 1

CBAD

Question 2

how to sketch modulus

Answer 2

draw normal graph without modulus and reflect negative bits in x axis

try and get into completing the square form

Question 3

how to find turning point of modulus

Answer 3

try and get into completing the square form – coefficient of 1 before x = then do -a, b to find turning point

Question 4

how to solve modulus equations

Answer 4

Do negative + positive of modulus function to find roots

Sketch to find how many solutions you’re looking for

Question 5

how to solve modulus inequalities

Answer 5

Question 6

Writing modulus without the modulus

Answer 6

Question 7

Writing no modulus in modulus form

o With gradient of 1…

Answer 7

Question 8

Writing no modulus in modulus form

o With gradient of 2 or more

Answer 8

Question 9

1/x and -1/x

Answer 9

Question 10

1/x3

Answer 10

looks same as 1/x - all odd powers

Question 11

1/ x squared and -1/ x squared

Answer 11

Question 12

all even power graphs

Answer 12

look same as 1/ x squared

Question 13

o larger ‘a’ value in y = a/x…

Answer 13

line further away from axis

Question 14

what is a function

Answer 14

• a mapping from the domain to the range such that for each x in the domain, there is a unique y in the range with f (x) = y

Only has 1 output

Question 15

types of mapping that are a function

Answer 15

One to one + many to one

Question 16

examples of all types of mapping

Answer 16

Question 17

even and odd function features

Answer 17

even - y axis is a line of symmetry

odd - rotational symmetry about the origin by 180

Question 18

composite functions

Answer 18

Work from right to left

Question 19

domain of composite functions

Answer 19

inner function brings its own baggage

AND

the inner function that has replaced the x in the outer function can NOT equal the banned values of the outer function

example

Question 20

inverse functions

Answer 20

o ONLY FOR ONE TO ONE FUNCTION

Question 21

what is inverse

Answer 21

reflection in y=x

Question 22

domain and range for inverse

Answer 22

they swap

Question 23

coordinates for inverse

Answer 23

they swap

Question 24

set notation for domain and range

Answer 24

Question 25

minimum/maximum point + line of symmetry for completing the square

Answer 25

Question 26

partial fractions normal

Answer 26

Question 27

partial fractions - comparing coefficients

Answer 27

Question 28

when should you long divide in partial fractions

Answer 28

Question 29

modulus equations where both sides are modulus

Answer 29

square both sides

MUST CHECK SOLUTIONS AFTER

Question 30

what is a self inverse function

Answer 30

get the same function back when we find its inverse

Question 31

maximum point

Answer 31

second derivative is less than 0

Question 32

minimum point

Answer 32

second derivative is more than 0

Question 33

concave down

Answer 33

second derivative is less than 0

Question 34

concave up

Answer 34

second derivative is more than 0

Question 35

point of inflection

Answer 35

first derivative / gradient same sign before and after point

second derivative changes sign before and after- concave up becomes concave down