Answer:
(4, 1)
Step-by-step explanation:
Since the first reflection is over the vertical line x=-3, the y-coordinate remains the same. The x-coordinate of A' will make the point (-3, 4) on the line of reflection be the midpoint between A and A':
(-3, 4) = (A +A')/2
2(-3, 4) -A = A' = (-6-(-7), 8 -4) = (1, 4)
The reflection over the line y=x simply interchanges the two coordinate values:
A'' = (4, 1)
Given:
The parent absolute function is
To find:
The new function if the parent function is translated up by 5 units and vertically stretched by a factor of 3.
Solution:
The translation is defined as
.... (1)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
Parent function is translated up by 5 units. So, b=5
It is vertically stretched by a factor of 3. So, k=3.
There is no horizontal shift. So, a=0.
Now, putting k=3, a=0 and b=5 in (1), we get
Therefore, the correct option is D.