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Write the equation for the transformation of \(f(x) = |x|\) described below: The function, \(g(x)\), is a result of translating right 7 units, shrunk vertically by a factor of 0.5, and translated up 5 units. a) \(g(x) = -0.5|x - 7| + 5\) b) \(g(x) = -|x - 7| + 5\) c) \(g(x) = -0.5|x + 7| + 5\) d) \(g(x) = -|x + 7| + 5\)

User JKupzig
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Final answer:

The correct transformation of function f(x) = |x|, after translating right by 7 units, shrinking vertically by a factor of 0.5, and then translating upwards by 5 units, is g(x) = 0.5 * |x - 7| + 5, none of the options (a) to (d) correctly represent this transformation.

Step-by-step explanation:

The student is asking for an equation that represents a transformation of the function f(x) = |x|. Given that g(x) is obtained from f(x) by a translation to the right by 7 units, a vertical shrink by a factor of 0.5, and then a translation upwards by 5 units, we can derive the transformed function step by step.

First, translating the function to the right by 7 units gives us f(x - 7) = |x - 7|. Next, the vertical shrink by a factor of 0.5 multiplies the function by 0.5, so we have 0.5 * |x - 7|. Finally, translating upwards by 5 units gives us 0.5 * |x - 7| + 5.

Hence, the correct equation for the transformation is g(x) = 0.5 * |x - 7| + 5, which matches none of the options provided by the student. An error may have occurred in the options given, as these transformations should not result in a sign change before the absolute value; therefore, we cannot accurately pick from options (a) to (d).

User Mhartl
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