To determine the range (or image) after translating the given points, we apply the translation to each of the coordinates. The translation is defined as 4 units left and 2 units up.

Translation Steps:

• 4 units left: Subtract 4 from the x-coordinate.
• 2 units up: Add 2 to the y-coordinate.

Let's apply this to each point in the domain:

1. Original point $(1, -5)$:

   • New x-coordinate: $1 - 4 = -3$
   • New y-coordinate: $-5 + 2 = -3$
   • Translated point: $(-3, -3)$

2. Original point $(-3, 7)$:

   • New x-coordinate: $-3 - 4 = -7$
   • New y-coordinate: $7 + 2 = 9$
   • Translated point: $(-7, 9)$

3. Original point $(-1, 3)$:

   • New x-coordinate: $-1 - 4 = -5$
   • New y-coordinate: $3 + 2 = 5$
   • Translated point: $(-5, 5)$

Translated Points (Range):

The resulting range after translation is $(-3, -3)$, $(-7, 9)$, and $(-5, 5)$.

Matching with Options:

The correct range from the options is $\boxed{(-3, -3), (-7, 9), (-5, 5)}$, which is the 3rd option.

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Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the effect of translating a figure on its shape and size?
2. How would a translation 3 units right and 5 units down affect the coordinates?
3. What is the difference between a translation and a rotation in coordinate transformations?
4. Can a translation change the orientation of a figure?
5. How would the translation affect a point located at the origin $(0, 0)$?

Tip: When translating points, always remember to adjust both the x and y coordinates accordingly, depending on the direction and magnitude of the translation.