Using the exponential function 2x + 3, what is the average rate of change between the values 1 ≤ x ≤ 5?
1 answer:
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Rotation of 180° clockwise change the coordinates from (x,y) to (-x,-y).
If the image point has the coordinates (3,-5).
It means (-x,-y) = (3,-5)
So pre-image point was (x,y) = (-3,5)
Hence, option C i.e. (-3,5) is the final answer.
If the image point has the coordinates (3,-5).
It means (-x,-y) = (3,-5)
So pre-image point was (x,y) = (-3,5)
Hence, option C i.e. (-3,5) is the final answer.
We can consider each unique 
as the as the 
-th unit vector. So your set 
can be considered as the vectors
Then check for independence your favorite way. In this case, I'll see if the linear map A of the new basis vectors doesn't map to a subspace via the determinant not being zero:
![det(A) = det \left ( \left [ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 3 \\ 0 & 1 & 4 \end{array}\right ] \right ) = 1(4-3) = 1](https://tex.z-dn.net/?f=%20det%28A%29%20%3D%20det%20%5Cleft%20%28%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bccc%7D%201%20%26%200%20%26%200%20%5C%5C%200%20%26%201%20%26%203%20%5C%5C%200%20%26%201%20%26%204%20%5Cend%7Barray%7D%5Cright%20%5D%20%5Cright%20%29%20%3D%201%284-3%29%20%3D%201)
So they are linear independent.
Then check for independence your favorite way. In this case, I'll see if the linear map A of the new basis vectors doesn't map to a subspace via the determinant not being zero:
So they are linear independent.