To find the corresponding points after shifting the graph of the function $y = f(x)$ up by 1 unit and to the left by 2 units, we need to apply these transformations to each of the given points.

Step-by-Step Solution

1. Shifting Up by 1 Unit:

   • When a graph is shifted up by 1 unit, the $y$-coordinates of each point increase by 1.

2. Shifting Left by 2 Units:

   • When a graph is shifted to the left by 2 units, the $x$-coordinates of each point decrease by 2.

Applying the Transformations

Given points:

1. $(-2, 3)$
2. $(5, -4)$

Point 1: $(-2, 3)$

• Shift left by 2 units: $x' = -2 - 2 = -4$
• Shift up by 1 unit: $y' = 3 + 1 = 4$
• New point: $(-4, 4)$

Point 2: $(5, -4)$

• Shift left by 2 units: $x' = 5 - 2 = 3$
• Shift up by 1 unit: $y' = -4 + 1 = -3$
• New point: $(3, -3)$

Final Answer

The corresponding points on the transformed graph are:

1. $(-4, 4)$
2. $(3, -3)$

Would you like more details or have any questions?

Related Questions to Explore

1. How do other types of transformations (such as reflections or stretches) affect the coordinates of points?
2. How can we represent these transformations algebraically using function notation?
3. What are the effects of shifting a function down and to the right?
4. How do combinations of transformations (like shifts and reflections) impact the final graph of a function?
5. How would these transformations change the graph if applied in a different order?

Tip: Visualizing transformations on graph paper can help you understand their effects more intuitively.