https://file.aiquickdraw.com/mathbot/file/1730305851072wsf7gfot.jpg

The original function shown on the graph is \( f(x) = \log_2 x \). The modified function given in the problem is \( f(x) = \log_2(x - 5) + 2 \).

To analyze how this modification affects the graph, let's break down each part:

1. **Horizontal Shift**: The expression \( x - 5 \) inside the logarithm shifts the graph horizontally. Specifically, it shifts the graph **5 units to the right**, since subtracting a constant from \( x \) inside a function moves the graph in the positive \( x \)-direction.

2. **Vertical Shift**: The \( +2 \) added outside the logarithmic function shifts the graph vertically. This shifts the graph **2 units up**, as adding a constant to the function moves it in the positive \( y \)-direction.

Therefore, the correct answers are:

- **A: Move 5 spaces right.**
- **C: Move 2 spaces up.**

Would you like more details or have any questions?

---

### Related Questions:
1. How would changing \( f(x) = \log_2(x) \) to \( f(x) = \log_2(x + 3) \) affect the graph?
2. What happens to the graph of \( f(x) = \log_2(x) \) if we change it to \( f(x) = -\log_2(x) \)?
3. How does multiplying the logarithmic function by a constant (e.g., \( 3 \log_2(x) \)) affect its graph?
4. What transformation occurs if we add a negative constant outside the function, such as \( f(x) = \log_2(x) - 4 \)?
5. How would the graph of \( f(x) = \log_2(x) \) change if it was modified to \( f(x) = \log_2(-x) \)?

---

### Tip:
When analyzing function transformations, remember that changes inside the function argument (like \( x - 5 \)) affect horizontal shifts, while changes outside (like \( +2 \)) affect vertical shifts.

Function f(x) = log₂x is shown on the graph. What effect would changing it to f(x) = log₂(x - 5) + 2 have on the graph? Select two that apply.

Explore the transformations applied to the logarithmic function f(x) = log₂x when it is changed to f(x) = log₂(x - 5) + 2. Learn how horizontal and vertical shifts affect the graph, with a step-by-step breakdown suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation