To find the image point of $(-7, 0)$ after a translation left 4 units and up 1 unit, you can follow these steps:

1. Translation Left 4 Units: Subtract 4 from the x-coordinate. $x = -7 - 4 = -11$

2. Translation Up 1 Unit: Add 1 to the y-coordinate. $y = 0 + 1 = 1$

Therefore, the image point after the translation is $(-11, 1)$.

Would you like more details or have any questions?

Here are some related questions you might find useful:

1. What is the image of the point (3, -2) after translating it right 5 units and down 3 units?
2. How do you find the image of a point after a reflection over the y-axis?
3. What is the general formula for translating a point in the coordinate plane?
4. How would you translate a point by a vector $\langle a, b \rangle$?
5. What is the effect of translating a point by $(0, 0)$ on the coordinate plane?

Tip: When translating a point, remember that left and right affect the x-coordinate, while up and down affect the y-coordinate.