Answer:
Equation for the curve in its final position is y = 2tan( x + 1 ) + 7.
Step-by-step explanation:
We have to find equation for the curve of y=tan(x) ,with following transformations:
vertically stretched by a factor of 2: y = 2tan(x)
shifted a distance of 1 units to the left: y = 2tan( x+1 )
translated 7 units upward: y = 2tan( x + 1 ) + 7
The equation for the curve in its final position is y = 2tan(x+2) + 7
Given the function f(x), if the function is stretched by a factor of "k", the resulting function will be kf(x)
If shifted a distance of "a" units to the left, and then translated b units upward, the resulting expression will be kf(x + a) + b
Given the function y = tan(x) if the function is vertically stretched by a factor of 2, the resulting function will be y = 2tan(x)
If shifted a distance of 2 units to the left, and then translated 7 units upward, the resulting expression will be y = 2tan(x + 2) + 7
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