Since vectors are defined by their direction and magnitude, what does having multiple starting and ending points to create the same vector tell you about how you can manipulate vectors on graphs.

Having multiple starting and ending points to create the same vector means keeping the length of the vector and direction same. So you can have multiple starting and ending points of a vector if their magnitude and direction are same.

Explanation:

To have same vector the magnitude and direction should match,

for example let us consider two dimensional vector a and b

vector a starts at (0,0) and ends at (5,5)

the magnitude will be 5.

vector a starts at (1,1) and ends at (6,6)

the magnitude will be 5 again and the direction will be same as vector a

so both vector have different starting and ending point but they are the same vectors as they have same magnitude and direction.

option number c is the right answer.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .