If g(x) is the f(x)=x after a vertical compression by 23, a shift left by 3, and a shift up by 4,

Let's go through the transformations step by step to find the equation for \( g(x) \).

### Step 1: Start with the function \( f(x) = x \).

### Step 2: Apply the vertical compression by 23
- A vertical compression by a factor of 23 means you multiply the function by \( \frac{1}{23} \).
- The function becomes: 
  \[
  f(x) = \frac{1}{23}x
  \]

### Step 3: Apply the shift left by 3
- Shifting the function to the left by 3 involves replacing \( x \) with \( (x + 3) \).
- The function becomes:
  \[
  g(x) = \frac{1}{23}(x + 3)
  \]

### Step 4: Apply the shift up by 4
- Shifting the function up by 4 involves adding 4 to the function.
- The final function becomes:
  \[
  g(x) = \frac{1}{23}(x + 3) + 4
  \]

### Final Equation:
- So, the equation for \( g(x) \) is:
  \[
  g(x) = \frac{1}{23}(x + 3) + 4
  \]

Would you like to find the slope and vertical intercept for this function as well?

### Related Questions:
1. How would the equation change if the function was shifted down instead of up?
2. What is the slope of the line after these transformations?
3. What is the vertical intercept after these transformations?
4. How would the equation be affected by a horizontal compression instead of a shift?
5. How do these transformations affect the graph of the function?

**Tip:** For multiple transformations, applying them in the correct order ensures accurate results.

Explore how vertical compression by 23, left shift by 3, and upward shift by 4 affect the function f(x)=x. Learn step-by-step with detailed explanations and equations for g(x).

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