What transformations are used to obtain g(x) from f(x)

g(x)= f(x)+5

g(x) = 2f(x)

g(x) = f(-2x)

g(x) = -3f(-x) +2

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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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