Use symmetry to graph the inverse of the function

The correct option is d.

Step-by-step explanation:

Let a function is f(x) and its inverse is f⁻¹(x). If both functions drawn on a coordinate plate than the graph of f(x) and f⁻¹(x) are mirror image of each other across the line y=x.

In other word the line y=x is the axis of symmetry of the graph of function and its inverse.

We need to find the correct graph that represent the function and its inverse.

Draw a line y=x in each graph as shown below.

From the below graph it is clear that only graph d represent the function and its inverse because both the functions are mirror image of each other across the line y=x.

Therefore the correct option is d.

it has changed from the width and the height.

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1