Question

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Answer 1

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Answer:

  (b)  g(x) = -f(x+3)

Step-by-step explanation:

The dashed-line graph is a reflection over the x-axis and a left-shift by 3 of the solid-line graph. To reflect the function over the x-axis, negate it.

  f(x) ⇒ -f(x) . . . . reflected over the x-axis

To translate a function to the right horizontally by "h" units, replace x in the function with (x-h). Here, we want a left shift, so h=-3. That is, x is replaced by (x+3).

Both transformations together give you ...

  g(x) = -f(x+3)