2 - chapter 3 - further transformations of graphs

Question 2

combining vertical transformations

Answer 2

y = f(x) into y = k f(x) + c
first multiply by k then add c

Question 3

combining horizontal transformations

Answer 3

y = f(x) to y = f(kx +c)
first add c (translate by -c)
then times by k (stretch factor 1/k)
OPPOSITE ORDER

Question 4

modulus

Answer 4

reverses sign of negative numbers
|x| = x when x>=0
= -x when x<0

Question 5

when drawing graphs with modulus

Answer 5

sketch y= f(x)
flip up when it hits the x axis (as to not have neg y values)

Question 6

using modulus notation

Answer 6

|x|<3 = -3<x<3
|x|>3 = x<-3 or x>3

|x-a|<b = a-b<x<a+b

Question 7

solving equations wiht modulus

Answer 7

draw graoh of each side
solution is where they meet
or if both sides are in modulus signs then square both sides as
|a|=|b| > a²=b²
BUT |a| = b does not =a²=b²