To translate the function $f(x) = x^2 + 5$ four units down, you subtract 4 from the entire function. This gives the transformed function:

$g(x) = f(x) - 4 = (x^2 + 5) - 4 = x^2 + 1$

Transformation Description:

• Original function: $f(x) = x^2 + 5$
• New function: $g(x) = x^2 + 1$
• This transformation moves the graph of $f(x)$ four units downward. The shape of the graph remains the same (a parabola opening upwards), but the vertex of the parabola shifts from $(0, 5)$ to $(0, 1)$.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:

1. How would you translate the function $f(x) = x^2 + 5$ four units up instead?
2. What is the effect of translating a function horizontally instead of vertically?
3. How would the equation change if you reflected the function over the x-axis?
4. How do you translate a function both horizontally and vertically?
5. How does translating a function affect its domain and range?

Tip: Vertical translations only affect the function’s output (the y-values) but do not change the shape of the graph.