Write an equation for the function that is described by the...

Write an equation for the function that is described by the given characteristics.
The shape of $f(x)=\sqrt{x}$, but shifted six units to the left and reflected in both the $x$ -axis and the $y$ -axis

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Key Concepts

Reflection

Reflection is a transformation that flips a graph over a specific axis. Reflecting in the x-axis inverts the output values (multiplying by -1), and reflecting in the y-axis inverts the input values (replacing x with -x). These operations change the orientation of the graph without altering its shape.

Square Root Function

The square root function, typically given as f(x) = ?x, is a basic radical function with a characteristic curved shape. Understanding its standard form is essential for applying transformations such as shifts and reflections to obtain a new function with modified properties.

Function Transformation

Function transformation is a process of altering the graph of a function through operations such as translations, reflections, stretches, and compressions. This concept is central to understanding how changes to the function’s formula affect its graph.

Horizontal Shift

A horizontal shift involves moving the graph of a function left or right. It is accomplished by replacing x with x plus or minus a constant. For a left shift, the function is expressed as f(x + c) where c is positive.

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