Let’s analyze each transformation and fill in the blanks:

1. $g(x) = f(x) + 1$:

   • Adding 1 outside the function means the graph is shifted 1 unit up.

2. $g(x) = f(x + 2)$:

   • Adding 2 inside the function argument means the graph is shifted 2 units left. (Remember: $(x + 2)$ shifts left because it affects the input oppositely.)

3. $g(x) = f(x) - 1$:

   • Subtracting 1 outside the function means the graph is shifted 1 unit down.

4. $g(x) = f(x - 1)$:

   • Subtracting 1 inside the function argument means the graph is shifted 1 unit right.

Final Answers:

1. $g(x) = f(x) + 1$: 1 unit up
2. $g(x) = f(x + 2)$: 2 units left
3. $g(x) = f(x) - 1$: 1 unit down
4. $g(x) = f(x - 1)$: 1 unit right

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Would you like further clarification or visual examples for these transformations?

Related Questions:

1. How does the sign of the shift inside the parentheses affect the direction?
2. What happens if we multiply $f(x)$ by a constant instead of adding/subtracting?
3. How would the transformation look if $g(x) = 2f(x)$?
4. How do these transformations affect the domain and range of $f(x)$?
5. Can you describe what happens for a transformation like $g(x) = f(-x)$?

Tip:

Shifts outside the function ($+/-$) affect the vertical direction, while shifts inside the parentheses ($+/-$) affect the horizontal direction and occur oppositely to their signs.