f(x) = |x| g(x) = |z| + 1 We can think of g as a translated (shifted) version of f. Complete the description of the transformation. Use nonnegative numbers.

Mathematics · Middle School · Thu Feb 04 2021

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To complete the description of the transformation of the function f(x) = |x| to obtain g(x) = |z| + 1, we need to consider what changes occur from f to g.

Firstly, notice that the variable inside the absolute value function has changed from 'x' to 'z'. This does not reveal any transformation if we don't have further information about how 'z' relates to 'x'. If we assume that 'z' is just another variable representing the same value as 'x', then the transformation does not involve any horizontal shift or stretch.

The more evident transformation is the "+ 1". This indicates a vertical translation (upward shift) of the graph of the function f(x). Specifically, for every x (or z), g(x) will have a value that is 1 unit greater than the value of f(x). There is no indication of a horizontal shift, reflection, or stretching based solely on the information given.

Therefore, the complete description of the transformation from f(x) to g(x) is a vertical translation (upward shift) of 1 unit.