Transformations of Inverse Trig Graphs

Adding a constant outside shifts the graph up by that amount.

Subtracting a constant outside shifts the graph down by that amount.

Adding outside: vertical shift up by π/6.

Replacing x with −x reflects a graph across the y-axis.

Multiplying the output by −1 reflects across the x-axis.

Subtracting outside: vertical shift down by π/4.

Subtracting π/2 outside shifts the graph down by π/2.

Replacing x with −x gives a reflection across the y-axis.

Multiplying by −1 reflects across the x-axis.

Adding π/2 outside shifts the graph upward by π/2.

Adding a positive constant outside moves the graph up.

Replacing x with −x reflects a graph across the y-axis.

Multiplying the output by −1 reflects across the x-axis.

Subtracting a constant outside moves the graph down.

Adding outside by π/2 shifts the graph up by π/2.

Adding π outside shifts the graph up by π.

Replacing x with x+2 shifts the graph left by 2.

Subtracting π/2 outside shifts the graph down by π/2.

Replacing x with x+1 shifts the graph left by 1.

y ↦ π − y reflects a graph across the line y = π/2.