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If we are given the graph of f(x) then:
(a) the graph of g(x)=f(x)+5 is the graph of f(x) translated (shifted) 5 units up (vertically).
(b) the graph of g(x)=2f(x) is the graph of f(x) with a vertical stretch of factor 2. (Multiply each y coordinate of f(x) by 2 to get the corresponding y-coordinate of g(x).)
(c) the graph of g(x)=f(-2x) is the graph of f(x) reflected across the y-axis and then compressed horizontally with a factor of 2.
(d): g(x)=-3f(-x)+2 is reflected over the y-axis (the -x) and reflected over the x-axis (since the 3 is negative). Then a vertical stretch of factor 3 followed by the vertical translation of 2.
1. g(x) shifted by 5 unit from f(x)
2. g(x) shift by f(x) from f(x). or can say double of f(x)
3. g(x) reflected by y-axis and horozontzal doubled
4. g(x) ,reflected by y-axis and x-axis ,triple the stretch and shift by 2 units.
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