algebra / functions Flashcards
how to transform graph
CBAD
how to sketch modulus
draw normal graph without modulus and reflect negative bits in x axis
try and get into completing the square form
how to find turning point of modulus
try and get into completing the square form – coefficient of 1 before x = then do -a, b to find turning point
how to solve modulus equations
Do negative + positive of modulus function to find roots
Sketch to find how many solutions you’re looking for
how to solve modulus inequalities
Writing modulus without the modulus
Writing no modulus in modulus form
o With gradient of 1…
Writing no modulus in modulus form
o With gradient of 2 or more
1/x and -1/x
1/x3
looks same as 1/x - all odd powers
1/ x squared and -1/ x squared
all even power graphs
look same as 1/ x squared
o larger ‘a’ value in y = a/x…
line further away from axis
what is a function
- 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
types of mapping that are a function
One to one + many to one
examples of all types of mapping
even and odd function features
even - y axis is a line of symmetry
odd - rotational symmetry about the origin by 180
composite functions
Work from right to left
domain of composite functions
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
inverse functions
o ONLY FOR ONE TO ONE FUNCTION
what is inverse
reflection in y=x
domain and range for inverse
they swap
coordinates for inverse
they swap
set notation for domain and range
minimum/maximum point + line of symmetry for completing the square
partial fractions normal
partial fractions - comparing coefficients
when should you long divide in partial fractions
modulus equations where both sides are modulus
square both sides
MUST CHECK SOLUTIONS AFTER
what is a self inverse function
get the same function back when we find its inverse
maximum point
second derivative is less than 0
minimum point
second derivative is more than 0
concave down
second derivative is less than 0
concave up
second derivative is more than 0
point of inflection
first derivative / gradient same sign before and after point
second derivative changes sign before and after- concave up becomes concave down
