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To tackle the questions in the image, let's break down each of the four listed features for the function \( g(x) = \log_2(x + 4) - 1 \):

### 1. **Vertical Asymptote**
- The vertical asymptote occurs where the argument of the logarithm is equal to zero because the logarithm function is undefined for non-positive numbers. For the function \( g(x) = \log_2(x + 4) - 1 \), the argument is \( x + 4 \).
- Setting \( x + 4 = 0 \), we find:
  \[
  x = -4
  \]
- Thus, the vertical asymptote is at \( x = -4 \).

### 2. **X- and Y-Intercepts**
- **X-Intercept:** Set \( g(x) = 0 \) and solve for \( x \).
  \[
  \log_2(x + 4) - 1 = 0
  \]
  \[
  \log_2(x + 4) = 1
  \]
  \[
  x + 4 = 2^1 = 2
  \]
  \[
  x = -2
  \]
  The x-intercept is at \( x = -2 \).

- **Y-Intercept:** Set \( x = 0 \) and solve for \( g(x) \).
  \[
  g(0) = \log_2(0 + 4) - 1
  \]
  \[
  g(0) = \log_2(4) - 1
  \]
  \[
  g(0) = 2 - 1 = 1
  \]
  The y-intercept is at \( y = 1 \).

### 3. **Transformations**
- The function \( g(x) = \log_2(x + 4) - 1 \) can be considered as a transformation of the parent function \( f(x) = \log_2(x) \).
- **Translation Left:** The \( +4 \) inside the logarithm translates the graph 4 units to the left.
- **Vertical Shift Down:** The \( -1 \) outside the logarithm shifts the graph down by 1 unit.

### 4. **Domain**
- The domain of the function \( g(x) = \log_2(x + 4) - 1 \) is determined by the argument of the logarithm, which must be positive:
  \[
  x + 4 > 0
  \]
  \[
  x > -4
  \]
- Therefore, the domain is \( x > -4 \), or in interval notation, \( (-4, \infty) \).

---

### Summary
1. **Vertical Asymptote:** \( x = -4 \).
2. **X-Intercept:** \( x = -2 \); **Y-Intercept:** \( y = 1 \).
3. **Transformations:** Left by 4 units, down by 1 unit.
4. **Domain:** \( x > -4 \).

Would you like more details or have any questions?

### Expanding Questions:
1. How would the vertical asymptote change if the function were \( g(x) = \log_2(x - 3) - 1 \)?
2. What effect does changing the base of the logarithm have on the graph?
3. If the function were \( g(x) = \log_2(x + 4) + 2 \), how would the transformations differ?
4. How do you find the range of \( g(x) \)?
5. What is the relationship between the domain and the vertical asymptote?

### Tip:
Always check the argument of the logarithmic function to determine where it is undefined, which will help you locate the vertical asymptote and establish the domain.

Explore how to analyze logarithmic functions, focusing on vertical asymptotes, transformations, and domain determination. This detailed guide covers examples like g(x) = log2(x + 4) - 1, illustrating key concepts in high school mathematics.

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