Question

f(x) = |×| g(x) = |×+9| – 5 We can think of g as a translated (shifted) version of f. Complete the description of the transformation. Use nonnegative numbers. To get the function g. shift f up/down by units and to the right/left v by units.

Answer 1

First we can check the value 9 that is added inside the absolute module operator.

This value is together with the variable x inside the operator, that is, from f(x) we can replace x by 'x + 9' in order to get the first part of g(x)

This addition of 9 to the value of x represents a horizontal translation of 9 units to the left.

Then, the subtraction of 5 units outside the absolute module operator is a addition/subtraction to the function, that is, we can subtract 5 units from f(x) in order to get this second part of f(x).

This subtraction of 5 units to the value of f(x) represents a vertical translation of 5 units down.

So the answer is:

To get the function g(x), shift f down by 5 units and to the left by 9 units.​