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).