SOLUTION: A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph.
f(x)= √x ; shift 6 units to the left
y=
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Question 1200477: A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph.
f(x)= √x ; shift 6 units to the left
y= (blank)
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Answer:
Explanation:
Imagine parent function square root curve is etched in stone on the wall.
As such, the curve itself cannot move.
Further, imagine that we can move the xy axis around like a target scope.
Imagine the axis is part of the camera that moves around.
Moving the xy axis 6 units to the right gives the illusion the curve moves 6 units to the left (even though the curve is still etched in stone).
Moving the xy axis 6 units to the right means each old input x is updated to the new input x+6
We go from to (replace each x with x+6)
Confirmation with a graph
in green
in blue
Desmos and GeoGebra are two graphing options I recommend.
Plug x = -6 into to find that:
Therefore, (-6,0) is on the curve
This is indicated as the left-most point of the blue curve shown above.
I'll let you try other x values.
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