Graphs and graph transformations

Question 1

Completing the square

Answer 1

half it
square it
take the square away

Question 2

quadratic graphs

Answer 2

positive = U
negative = n

Question 3

cubic graphs

Answer 3

wiggle / wave

Question 4

reciprocal graphs

Answer 4

in opposite quadrants, lines never meet

Question 5

Graph transformation - f (x) + a

Answer 5

y coord has a added to it
x remains same

moves up a units

Question 6

Graph transformation - f (x) - a

Answer 6

y coords have a subtracted from the
x coord remain same

moves downwards a units

Question 7

Graph transformation - f (x+a)

Answer 7

x cooords have a subtracted from them
y coords remain same

moves a units to left

Question 8

Graph transformation - f (x+a)

Answer 8

x cooords have a subtracted from them
y coords remain same

moves a units to left

Question 9

Graph transformation - f (x-a)

Answer 9

x cooords have a added to them
y coords remain same

moves a units to right

Question 10

Graph transformation - af (x)

Answer 10

x coords remain same
y coords multiplied by a

stretched by factor of a up y-axis

Question 11

Graph transformation - f (ax)

Answer 11

x coords divide by a
y coord remain same

stretched by factor of 1/a along x axis

Question 12

Graph transformation - -f (x)

Answer 12

x coords remain same
y coords change sign (+ -> -) or (- -> +)

reflected in x axis

Question 13

Graph transformation - f(-x)

Answer 13

x coords change signs
y coords remain same

reflected in y axis

Question 14

Graph transformation rules

Answer 14

If change inside bracket with x - effect on x coordinates and does opposite
If change on outside effect is on y coordinates and it does what you expect