trig graphs and graph transformations

sine graph

cosine graph

tan graph

transformation: f(x + k)

f(x) is moved k to the right

transformation: f(x - k)

f(x) is moved k to the left

transformation: f(x) + k

f(x) is moved k upwards

transformation: f(x) - k

f(x) is moved k downwards

transformation: af(x) when a is bigger than 1

f(x) is stretched vertically by the factor of a

transformation: af(x) when a is less than 1 and bigger than 0

f(x) is squashed vertically by the factor of a

transformation: af(x) when a is less than 0

f(x) is reflected in the x axis

transformation: f(ax) when a is bigger than 1

f(x) is squashed horizontally by a factor of a

transformation: f(ax) when a is less than 1 and bigger than 0

f(x) is stretched horizontally by a factor of a

transformation: f(ax) when a is less than 0

f(x) is reflected in the y axis