Given that f(x) = square root x, which equation describes the graph of function g?
Answer (2)
To determine the equation for g ( x ) , we need to apply transformations to f ( x ) = x such as translations, reflections, or stretches. Each transformation affects the appearance of the graph differently, resulting in various forms of g ( x ) based on the specifics of the transformation used. Identifying the exact transformation instruction is key to finding the correct equation for g ( x ) .
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To determine the equation that describes the graph of the function g ( x ) based on f ( x ) = x , we need more information about how g ( x ) is derived from f ( x ) . Typically, graphs of functions are related through transformations such as translation, reflection, stretching, or compression. Here's an explanation of each type of transformation:
Translation - A shift in the graph's position without changing its shape. For example, shifting f ( x ) up by 2 units results in g ( x ) = x + 2 .
Reflection - A flip over a specific axis. Reflecting f ( x ) over the x-axis changes it to g ( x ) = − x .
Stretching/ Compression - Changing the graph's size proportionally in the vertical or horizontal direction. Vertical stretching by a factor of 2 changes the function to g ( x ) = 2 x .
Horizontal/Vertical Shifts - Moving the graph left or right on the x-axis. For example, shifting it 3 units to the right results in g ( x ) = x − 3 .
Given specific transformation instructions, you can find the equation for g ( x ) . If such transformations apply, replace 'shift', 'reflect', 'stretch', etc., with the correct descriptors for the transformation according to an assigned value or conditions.
