5 - using graphs

Question 1

how to find intersections of the graph

Answer 1

simultaneous equations

Question 2

how to use discriminant with intersections

Answer 2

use discriminant to input simultaneous equations to see the number of intersections

Question 3

transformations

Answer 3

f(x) +a = a units up
f(x +a) = a units left
fa(x) = stretch parallel to the y axis by SF a
f(ax) - strech parallel to the x axis by 1/a
-f(x) = reflection in x axis
f(-x) = reflection in y axis

Question 4

reciprocal graphs

Answer 4

eg a/x
have asymptotes x=0 and y=0
if they are transformed just change the asymptote then draw the graph

Question 5

a/x^2

Answer 5

reciprocal in the top two quadrants as you can have no negative y values (x is squared)

Question 6

direct proportion

Answer 6

y = kx
ratio of quantities is constant

Question 7

inverse proportion

Answer 7

y = k/x
product of quantities is constant