To solve for the transformation of the function $y = f(x) + 3$, we need to understand how the graph of $f(x)$ is modified when we add 3 to it. Let's break this down:

Transformation Description:

1. Vertical Shift: The expression $y = f(x) + 3$ represents a vertical shift of the graph of $f(x)$.

2. Upward Shift: Adding 3 to $f(x)$ means that every point on the graph of $f(x)$ is moved up by 3 units.

Visual Representation:

If you have the graph of $f(x)$, to obtain the graph of $y = f(x) + 3$:

• Take each point $(x, f(x))$ on the graph.
• Move it vertically to $(x, f(x) + 3)$.

Example:

If $f(x) = x^2$, then: $y = f(x) + 3 = x^2 + 3.$

• The original graph $y = x^2$ (a parabola) is shifted upward by 3 units.

Would you like to see more examples or have a specific function you'd like to transform?

Related Questions:

1. What would the graph look like for $y = f(x) - 2$?
2. How does the transformation $y = f(x + 3)$ differ from $y = f(x) + 3$?
3. If $y = 2f(x)$, what type of transformation does this represent?
4. What happens to the graph of $y = f(x)$ if it is reflected across the x-axis and shifted downward by 4 units?
5. How can you describe the transformation for $y = f(-x) - 1$?

Tip: When dealing with transformations, always consider the type (shift, stretch, or reflection) and the direction (horizontal or vertical) to understand their effects on the graph.