f(x) = x^2 + 5 ; translate the function 4 units down. Describe the Transformation. 

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.

f(x) = x^2 + 5 ; translate the function 4 units down. Describe the Transformation.

Learn how to translate the quadratic function f(x) = x^2 + 5 four units down. This guide explains the transformation step-by-step, showing how the function changes to g(x) = x^2 + 1 and how the graph shifts vertically while retaining its shape. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation