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Let's analyze the given problem step by step:

The function \( g(x) = |x - 1| + 4 \) is presented.

### Part (a) Identify the parent function \( f(x) \):

The parent function here is the **absolute value function**. This is because \( g(x) \) is a transformation of the absolute value function. The general form of the absolute value function is:

\[
f(x) = |x|
\]

### Part (b) Describe the sequence of transformations from \( f \) to \( g \):

The transformations applied to the parent function \( f(x) = |x| \) are as follows:

1. **Horizontal shift**: The expression \( |x - 1| \) indicates a **horizontal shift of 1 unit to the right**.
2. **Vertical shift**: The addition of 4 in \( |x - 1| + 4 \) means the graph is shifted **4 units upward**.

So, the correct transformations are:
- Horizontal shift of 1 unit to the right.
- Vertical shift of 4 units upward.

### Part (c) Sketch the graph of \( g(x) \):

The graph of \( g(x) = |x - 1| + 4 \) is a V-shaped graph. It is derived from the absolute value function, but the vertex (lowest point) of the V is shifted 1 unit to the right (to \( x = 1 \)) and 4 units up (to \( y = 4 \)).

Would you like me to provide more details or clarify anything? 

Here are 5 related questions to expand on this:

1. How would the graph change if the function was \( g(x) = |x + 1| + 4 \)?
2. What effect does multiplying the function by a negative sign have on the graph of \( f(x) = |x| \)?
3. How do horizontal shifts differ from vertical shifts in transformations?
4. Can you describe how reflections in the x-axis and y-axis would alter the graph of \( g(x) \)?
5. How do transformations affect the domain and range of absolute value functions?

**Tip**: When graphing absolute value functions, always identify the vertex first, as it determines the overall shape and placement of the graph.

The function g is related to one of the parent functions. g(x) = |x - 1| + 4. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g.

Learn how to transform the parent absolute value function f(x) = |x| into g(x) = |x - 1| + 4. This involves horizontal and vertical shifts. Ideal for students in Grades 9-11.

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