The graph of y=sqrt3: -8x-4 is a horizontal stretch by a factor of 8 and a reflection across the x-axis of the parent function y=sqrt(x).
Rewriting the function to determine the transformation:
Multiply the argument by -1: The argument of the square root function is -8x-4.
Multiplying both sides by -1 gives:
-y = sqrt[3](8x+4)
Isolate the square root: Divide both sides by -1:
y = -sqrt[3](8x+4)
Scale the argument: The argument of the square root is now 8x+4.
This is equivalent to scaling the argument in the parent function by a factor of 8.
Reflect the output: Since the function is multiplied by -1, the output is reflected across the x-axis.
Transformation of the graph compared to the parent function:
Horizontal stretch: The graph is stretched horizontally by a factor of 8.
This means that for every one unit the input changes, the output changes by 8 units instead of 1 unit.
Reflection across the x-axis: The graph is reflected across the x-axis.
This means that the y-values are flipped for all corresponding x-values.
No vertical shift: There is no vertical shift, so the graph remains at the same y-intercept as the parent function.
Question
Explain how to rewrite the function shown in order to determine the transformation of the parent function. Then, describe the transformation of the graph compared to the parent function. y=sqrt[3](-8x-4)