Graph stretches, reflections and translations

Translation up 1

f(x)+1

Translation down 1

f(x)-1

Translation left 1

f(x+1)

Translation right 1

f(x-1)

reflection across the y-axis

f(-x)

reflection across the x-axis

-f(x)

vertical stretch by scale factor of 2

2f(x)

horizontal compression

f(2x)

vertical compression by scale factor of 1/2

1/2f(x)

horizontal stretch

f(1/2x)

translation right 3 & up 4

translation left 2 and reflection across the x-axis

translation left 5 & up 2 and reflection across the y-axis

translation left 1 and reflection across the x-axis

translation left 3 and vertical compression by a factor of 1/2

translation left 4 & down 6

translation up 3 and vertical compression by a factor of 1/2

translation left 2 & up 5 and reflection across the y-axis

translation left 2 and vertical stretch by a factor of 4 and reflection across the y-axis

translation up 2 and vertical stretch by a factor of 3

translation left 1 and vertical stretch by a factor of 2 and reflection across the x-axis

translation left 1 and vertical stretch by a factor of 3

translation right 2 & down 3 and a horizontal stretch

translation left 1 and vertical stretch by a factor of 2 and reflection across the y-axis

translation right 2 & up 5

translation left 3 & up 4 and vertical compression by a factor of 1/2

translation right 2 & up 3

translation left 5 & up 1 and reflection across the x-axis