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.