Horizontal shift because g(x)=f(x+1) 1 unit left
Vertical shift because g(x)=f(x+1)-4 4 units down
Reflected across x-axis because g(x)=-f(x)
Vertically stretched because g(x)=3(f(x))
Step-by-step explanation:
We need to identify which transformation have been preformed on a graph of f(x)=x2 to obtained the graph of g(x) =-3(x+1)2-4?
Rules for transformation:
Horizontal shift: depends on the value h
if g(x)=f(x+h) then: the graph is shifted left h units
if g(x)=f(x-h) then: the graph is shifted right h units
Vertical Shift: depends on the value k
if g(x)=f(x)+k then: the graph is shifted up k units
if g(x)=f(x)-k then: the graph is shifted down k units
Reflection:
if g(x)=-f(x) then graph is reflected at x-axis
if g(x)=f(-x) then graph is reflected at y-axis
Vertical Stretch:
if g(x)=c.f(x) then graph is vertically stretched.
In the given question:
f(x)= x^2
g(x)=-3(x+1)^2-4
Applying the above rules of transformation:
The graph is:
Horizontal shift because g(x)=f(x+1) 1 unit left
Vertical shift because g(x)=f(x+1)-4 4 units down
Reflected across x-axis because g(x)=-f(x)
Vertically stretched because g(x)=3(f(x))
Keywords: Transformations
Learn more about Transformations at:
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