Transformations of Inverse Trig Graphs

1) The graph of y = arcsin(x) + π/4 is obtained from y = arcsin(x) by which transformation?

Reflection over the x-axis

Horizontal shift left by π/4

Vertical shift upward by π/4

Vertical shift downward by π/4

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

Explanation

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

2) The graph of y = arccos(x) − π/3 is obtained from y = arccos(x) by which transformation?

Reflection over the x-axis

Horizontal shift right by π/3

Vertical shift downward by π/3

Vertical shift upward by π/3

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

Explanation

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

3) The graph of y = arctan(x) + π/6 is obtained from y = arctan(x) by which transformation?

Vertical shift upward by π/6

Vertical shift downward by π/6

Horizontal shift right by π/6

Reflection over the x-axis

Adding outside: vertical shift up by π/6.

Explanation

Adding outside: vertical shift up by π/6.

4) The graph of y = arcsin(−x) is obtained from y = arcsin(x) by which transformation?

Horizontal shift right by π

Reflection across the x-axis

Vertical shift downward by π

Reflection across the y-axis

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

Explanation

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

5) The graph of y = −arccos(x) is obtained from y = arccos(x) by which transformation?

Vertical shift downward by π/2

Reflection over the x-axis

Horizontal shift left by π/2

Vertical shift upward by π/2

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

Explanation

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

6) The graph of y = arctan(x) − π/4 is obtained from y = arctan(x) by which transformation?

Reflection over the y-axis

Vertical shift downward by π/4

Horizontal shift left by π/4

Reflection over the x-axis

Subtracting outside: vertical shift down by π/4.

Explanation

Subtracting outside: vertical shift down by π/4.

7) The graph of y = arcsin(x) − π/2 is obtained from y = arcsin(x) by which transformation?

Reflection across the line y = x

Vertical shift upward by π/2

Vertical shift downward by π/2

Reflection across the x-axis

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

Explanation

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

8) The graph of y = arccos(−x) is obtained from y = arccos(x) by which transformation?

Reflection across the y-axis

Reflection across the x-axis

Vertical shift upward by π

Reflection across the line y = x

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

Explanation

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

9) The graph of y = −arctan(x) is obtained from y = arctan(x) by which transformation?

Reflection across the y-axis

Reflection across the x-axis

Vertical shift upward by π

Horizontal shift right by π/2

Multiplying by −1 reflects across the x-axis.

Explanation

Multiplying by −1 reflects across the x-axis.

10) The graph of y = arcsin(x) + π/2 is obtained from y = arcsin(x) by which transformation?

Vertical shift upward by π/2

Vertical shift downward by π/2

Reflection over the x-axis

Reflection over the y-axis

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

Explanation

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

11) The graph of y = arccos(x) + π/2 is obtained from y = arccos(x) by which transformation?

Reflection across the x-axis

Vertical shift downward by π/2

Reflection across the y-axis

Vertical shift upward by π/2

Adding a positive constant outside moves the graph up.

Explanation

Adding a positive constant outside moves the graph up.

12) The graph of y = arctan(−x) is obtained from y = arctan(x) by which transformation?

Reflection across the y-axis

Vertical shift upward by π

Reflection across the x-axis

Vertical shift downward by π

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

Explanation

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

13) The graph of y = −arcsin(x) is obtained from y = arcsin(x) by which transformation?

Reflection across the y-axis

Reflection across the x-axis

Vertical shift downward by π/2

Horizontal shift left by π/2

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

Explanation

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

14) The graph of y = arccos(x) − π/2 is obtained from y = arccos(x) by which transformation?

Reflection across the x-axis

Vertical shift downward by π/2

Vertical shift upward by π/2

Reflection across the y-axis

Subtracting a constant outside moves the graph down.

Explanation

Subtracting a constant outside moves the graph down.

15) The graph of y = arctan(x) + π/2 is obtained from y = arctan(x) by which transformation?

Vertical shift upward by π/2

Vertical shift downward by π/2

Reflection across the line y = x

Reflection across the x-axis

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

Explanation

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

16) The graph of y = arcsin(x) + π is obtained from y = arcsin(x) by which transformation?

Reflection across the y-axis

Vertical shift downward by π

Reflection across the x-axis

Vertical shift upward by π

Adding π outside shifts the graph up by π.

Explanation

Adding π outside shifts the graph up by π.

17) The graph of y = arccos(x + 2) is obtained from y = arccos(x) by which transformation?

Vertical shift upward by 2

Horizontal shift right by 2

Horizontal shift left by 2

Vertical shift downward by 2

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

Explanation

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

18) The graph of y = arctan(x) − π/2 is obtained from y = arctan(x) by which transformation?

Vertical shift downward by π/2

Vertical shift upward by π/2

Reflection over the x-axis

Reflection over the y-axis

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

Explanation

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

19) The graph of y = arcsin(x + 1) is obtained from y = arcsin(x) by which transformation?

Reflection across the y-axis

Horizontal shift right by 1

Vertical shift upward by 1

Horizontal shift left by 1

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

Explanation

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

20) The graph of y = π − arccos(x) is obtained from y = arccos(x) by which transformation?

Reflection across the horizontal line y = π/2

Reflection across the y-axis

Vertical shift upward by π

Reflection across the x-axis

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

Explanation

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