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2 answers:
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Answer:
Scale factor 2.
Step-by-step explanation:
The vertices of shape I are (2,1), (3,1), (4,3), (3,3), (3,2), (2,2), (2,3), (1,3).
The vertices of shape II are (-4,-2), (-6,-2), (-8,-6), (-6,-6), (-6,-4), (-4,-4), (-4,-6), (-2,-6).
Consider shape I is similar to shape II. The sequence that maps shape I onto shape II is a 180 degree clockwise rotation about the origin, and then a dilation by a scale factor of k.
Rule of 180 degree clockwise rotation about the origin:
The vertices of shape I after rotation are (-2,-1), (-3,-1), (-4,-3), (-3,-3), (-3,-2), (-2,-2), (-2,-3), (-1,-3).
Rule of dilation by a scale factor of k.
So,
We know that, the image of (-2,-1) after dilation is (-4,-2). So,
On comparing both sides, we get
Therefore, the scale factor is 2.
Question 1:
For this case we must findknowing that:
By definition we have that, be two functions f (x) and g (x), then the composite function of f with g is:
In this case, they ask us for the function composed of g with f:
So, we have:
ANswer:
Question 2:
For this case, we must find the inverse function of , given by:
To do this, replace g(x) with y:
We exchange variables:
We solve for "y":
Replace "y" with
So, we have:
Answer:
Question 3:
For this case, we have by definition, the domain of a function f (x), is the set of all the values for which the function is defined.
We must find the domain of the following function:
It is observed that the function is not defined for
Then the domain is given by all the values of x, except 0.
for any integer n
Answer:
All numbers, except