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=

Algebra ->  Rational-functions -> 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=      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: y+=+sqrt%28x%2B6%29


Explanation:
Imagine parent function square root curve y+=+sqrt%28x%29 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 y+=+sqrt%28x%29 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 y+=+sqrt%28x%29 to y+=+sqrt%28x%2B6%29 (replace each x with x+6)

Confirmation with a graph
%0D%0Agraph%28300%2C300%2C-8%2C5%2C-4%2C4%2C-100%2Csqrt%28x%29%2Csqrt%28x%2B6%29%29%0D%0A
y+=+sqrt%28x%29 in green
y+=+sqrt%28x%2B6%29 in blue
Desmos and GeoGebra are two graphing options I recommend.

Plug x = -6 into y+=+sqrt%28x%2B6%29 to find that:
y+=+sqrt%28x%2B6%29
y+=+sqrt%28-6%2B6%29
y+=+sqrt%280%29
y+=+0
Therefore, (-6,0) is on the curve y+=+sqrt%28x%2B6%29
This is indicated as the left-most point of the blue curve shown above.
I'll let you try other x values.